Statistics Questions

point s possible The data on the right represent the number of live multiple delivery births three or more babies in a particular year for women 15 to 54 years old Use the data to complete parts a through d below CIE P 30 to 39 Type an integer or decimal rounded to three decimal places as needed P not 30 to 39 Type an integer or decimal rounded to three decimal places as needed Age 15 19 20 24 25 29 30 34 35 39 P less than 45 Type an integer or decimal rounded to three decimal places as needed 40 44 45 54 test Number of Multiple Births a Determine the probability that a randomly selected multiple birth for women 15 54 years old involved a mother 30 to 39 years old P at least 40 Type an integer or decimal rounded to three decimal places as needed b Determine the probability that a randomly selected multiple birth for women 15 54 years old involved a mother who was not 30 to 39 years old 92 509 1629 2838 1842 c Determine the probability that a randomly selected multiple birth for women 15 54 years old involved a mother who was less than 45 years old 379 119 d Determine the probability that a randomly selected multiple birth for women 15 54 years old involved a mother who was at least 40 years old Interpret this result Is it unusual Find the probability that a randomly selected multiple birth for women 15 54 years old involved a mother who was at least 40 years old Interpret this result Select the correct choice below and fill in the answer box to complete your choice Type a whole number OB If 1000 multiple births for women 15 54 years old were randomly selected exactly a mother who was at least 40 years old OA If 1000 multiple births for women 15 54 years old were randomly selected we would expect about them to involve a mother who was at least 40 years old of of them would involve sa multiple birth involving a mother who was at least 40 years old unusual A No because the probability of a multiple birth involving a mother who was at least 40 years old is greater than 0 05 OB Yes because the probability of a multiple birth involving a mother who was at least 40 years old is greater than 0 05 OC No because the probability of a multiple birth involving a mother who was at least 40 years old is less than 0 05 tisls birth involving a mother who was at least 40 years old is less than

The table shows the outcome of car accidents in a certain state for a recent year by whether or not the driver wore seat belt Driver Survived Driver Died Total The probability as a decimal is Round to three decimal places as needed Wore Seat No Seat Belt Belt 411 455 The probability as a fraction is Tyne an integer or a simplified fraction 166 330 Total 510 1693 2203 411 965 168 023 579 988 Find the probability of not surviving a car accident given that the driver wore a seat belt 577 785

The time it takes a person to wash the dishes is uniformly distributed between 5 minutes and 13 minutes What is the probability that a randomly selected event of washing dishes will take a person between 8 and 12 minutes Round your answer accurate to two decimal places

Suppose that the value of a stock varies each day from 12 82 to 15 17 with a uniform distribution Find the third quartile i e 75 of all days the stock is below what value Round your answer to the nearest cent

The uniform distribution of a random variable X is given in the figure below 0 1 X 2 From the figure what is the probability that a randomly selected X is between 0 86 and 1 44 Round you answer to two decimal places

Suppose this distribution represents the probabilities of extending our class a minutes past the end of class time 0 20 0 1 2 The variable is continuous 3 4 5 because there exist fractional amounts of time The total area of the distribution rectangle is and the sum of all the probabilities should be 1 which makes sense as it is a probability distribution The probability in decimal form of the class extending 3 or more minutes beyond the end time is found by determining the area to the right of a 3 or the complement of the area to the left The probability in decimal form of the class extending 3 or less minutes beyond the end time is found by determining the area to the left of x 3 Remember that when we read our distribution tables for many of our distributions the area quoted in the tables is to the left so it is important to be able to recognize the need for using the complement to find the area to the right

At December 31 Assets Cash Accounts receivable net Merchandise inventory Prepaid expenses Plant assets net Total assets Liabilities and Equity Accounts payable Long term notes payable Common stock 10 par value Retained earnings Total liabilities and equity Interest expense Income tax expense Total costs and expenses Net income Current Year 32 000 87 400 111 500 10 250 278 000 519 150 Earnings per share 1 Year Ago 128 800 97 500 162 000 130 850 73 750 101 750 162 000 99 950 519 150 437 450 Current Year 36 500 63 000 80 200 9 250 248 500 437 450 454 450 230 950 11 200 9 450 The company s income statements for the Current Year and 1 Year Ago follow For Year Ended December 31 Sales Cost of goods sold Other operating expenses 745 000 706 050 38 950 2 40 2 Years Ago For both the Current Year and 1 Year Ago compute the following ratios 37 000 49 000 54 500 4 100 228 000 372 600 1 a Compute profit margin ratio for the current year and one year ago 1 b Did profit margin improve or worsen in the Current Year versus 1 Year Ago 50 800 82 800 162 000 77 000 372 600 403 200 151 200 13 000 8 700 1 Year Ago 630 000 576 100 53 900 3 33

2 ints Express the following comparative income statements in common size percents Using the common size percents which item is most responsible for the decline in net income Complete this question by entering your answers in the tabs below Income Statement Reason for Decline in Net Income Express the following comparative income statements in common size percents Note Round your percentage answers to 1 decimal place Sales Cost of goods sold Gross profit Operating expenses Net income GOMEZ CORPORATION Comparative Income Statements For Years Ended December 31 Current Year Current Year Answer is complete but not entirely correct 740 000 565 400 174 600 129 200 45 400 Prior Year 100 0 640 000 76 4 280 000 23 6 360 000 17 5 258 800 6 1 101 200 33 Prior Year 100 0 icate completion 76 4 x 23 6 x 17 5 x 6 1 X Return to quest

The duration of a professor s class has continuous uniform distribution between 49 2 minutes and 55 5 minutes If one class is randomly selected and the probability that the duration of the class is longer than a certain number of minutes is 0 582 then find the duration of the randomly selected class i e if P x c 0 582 then find c where c is the duration of the randomly selected class Round your answer to one decimal places minutes

Given the uniform distribution below f x 0 1 2 3 4 5 6 7 8 9 10 11 12 X a What is the height of the function f x Give your answer as a reduced fraction b What is the probability of the shaded region Give your answer as a reduced frac

Suppose X is a continuous random variable Then the probability that X is exactly 6 is P X 6

Given the uniform distribution below find the probability of the shaded region Give your answer in fraction form 19

Use the skewed graph below to answer the questions Please use capital letters in your answer A B a Which letter represents the mean b Which letter represents the median c Which letter represents the mode C

Consider the density curve plotted below PDF X 0 11 0 1 0 09 0 08 0 07 0 06 0 05 0 04 0 03 0 02 0 01 29 30 Find P X 33 Find P X35 31 32 33 Density Curve 34 35 X 36 37 38 39 4

Consider the density curve plotted below PDF X 5 4 3 2 1 Find P X 0 16 Find P X 0 24 0 08 Density Curve 0 16 X 0 24 0 32 0 4 Q

A survey found that women s heights are normally distributed with mean 63 6 in and standard deviation 2 5 in A branch of the military requires women s heights to be between 58 in and 80 in a Find the percentage of women meeting the height requirement Are many women being denied the opportunity to join this branch of the military because they are too short or too tall b If this branch of the military changes the height requirements so that all women are eligible except the shortest 1 and the tallest 2 what are the new height requirements Click to view page 1 of the table Click to view page 2 of the table a The percentage of women who meet the height requirement is Round to two decimal places as needed Are many women being denied the opportunity to join this branch of the military because they are too short or too tall O A No because only a small percentage of women are not allowed to join this branch of the military because of their height O B Yes because the percentage of women who meet the height requirement is fairly large OC No because the percentage of women who meet the height requirement is fairly small OD Yes because a large percentage of women are not allowed to join this branch of the military because of their height b For the new height requirements this branch of the military requires women s heights to be at least in and at most in Bound to one donimol pia

Assume that females have pulse rates that are normally distributed with a mean of 75 0 beats per minute and a standard deviation of o 12 5 beats per minute Complete parts a through c below a If 1 adult female is randomly selected find the probability that her pulse rate is less than 79 beats per minute The probability is Round to four decimal places as needed b If 4 adult females are randomly selected find the probability that they have pulse rates with a mean less than 79 beats per minute The probability is Round to four decimal places as needed c Why can the normal distribution be used in part b even though the sample size does not exceed 30 OA Since the mean pulse rate exceeds 30 the distribution of sample means is a normal distribution for any sample size OB Since the distribution is of individuals not sample means the distribution is a normal distribution for any sample size OC Since the original population has a normal distribution the distribution of sample means is a normal distribution for any sample size OD Since the distribution is of sample means not individuals the distribution is a normal distribution for any

Assume that hybridization experiments are conducted with peas having the property that for offspring there is a 0 25 probability that a pea has green pods Assume that the offspring peas are randomly selected in groups of 26 Complete parts a through c below a Find the mean and the standard deviation for the numbers of peas with green pods in the groups of 26 The value of the mean is peas Type an integer or a decimal Do not round The value of the standard deviation is o Round to one decimal place as needed Values of Round to one decimal place as needed b Use the range rule of thumb to find the values separating results that are significantly low or significantly high peas peas or fewer are significantly low The result Round to one decimal place as needed Values of peas or greater are significantly high Round to one decimal place as needed c Is a result of 1 peas with green pods a result that is significantly low Why or why not significantly low because 1 peas with green pods is peas

A clinical test on humans of a new drug is normally done in three phases Phase I is conducted with a relatively small number of healthy volunteers For example a phase I test of a specific drug involved only 5 subjects Assume that we want to treat 5 healthy humans with this new drug and we have 10 suitable volunteers available Complete parts a through c below a If the subjects are selected and treated in sequence so that the trial is discontinued if anyone displays adverse effects how many different sequential arrangements are possible if 5 people are selected from the 10 that are available Choose the correct answer below OA 252 OB 3 628 800 OC 30 240 OD 120 b If 5 subjects are selected from the 10 that are available and the 5 selected subjects are all treated at the same time how many different treatment groups are possible different treatment groups possible c If 5 subjects are randomly selected and treated at the same time what is the probability of selecting the 5 youngest subjects P selecting the 5 youngest subjects Type an integer or a simplified fraction There are

Points 0 of 1 The probability of having at least two male children is Type an integer or a simplified fraction Save You select a family with three children If M represents a male child and F a female child the set of equally likely outcomes for the children s genders is shown below Find the probability of selecting a family with at least two male children MMM MMF MFM MFF FMM FMF FFM FFF

The probability of having exactly one female child is Type an integer or a simplified fraction Points 0 of 1 You select a family with four children If M represents a male child and F a female child the set of equally likely outcomes for the children s genders is FFFF FFFM FFMF FMFF MFFF MFFM MFMF MMFF FFMM FMFM FMMF FMMM MFMM MMFM MMMF MMMM Find the probability of selecting a family with exactly one female child Save

A water taxi carries passengers from harbor to another Assume that weights of passengers are normally distributed with a mean of 184 lb and a standard deviation of 35 lb The water taxi has a stated capacity of 25 passengers and the water taxi was rated for a load limit of 3500 lb Complete parts a through d below a Given that the water taxi was rated for a load limit of 3500 lb what is the maximum mean weight of the passengers if the water taxi is filled to the stated capacity of 25 passengers The maximum mean weight is 140 lb Type an integer or a decimal Do not round b If the water taxi is filled with 25 randomly selected passengers what is the probability that their mean weight exceeds the value from part a The probability is 1 Round to four decimal places as needed c If the weight assumptions were revised so that the new capacity became 20 passengers and the water taxi is filled with 20 randomly selected passengers what is the probability that their mean weight exceeds 175 lb which is the maximum mean weight that does not cause the total load to exceed 3500 lb The probability is 0 8749 Round to four decimal places as needed d Is the new capacity of 20 passengers safe Since the probability of overloading is the new capacity to be safe enough

Refer to the accompanying table which describes the number of adults in groups of five who reported sleepwalking Find the mean and standard deviation for the numbers of sleepwalkers i groups of five Click the icon to view the data table The mean is sleepwalker s Round to one decimal place as needed The standard deviation is sleepwalker s Round to one decimal place as needed Table of numbers of sleepwalkers and probabilities X01234 P x 0 169 0 357 0 304 0 135 0 031 X

When testing for current in a cable with ten color coded wires the author used a meter to test five wires at a time How many different tests are required for every possible pairing of five wires The number of tooto

If radio station call letters must begin with either K or W and must include either two or three additional letters how many different possibilities are there There are different possibilities Simplify your answer

When a man observed a sobriety checkpoint conducted by a police department he saw 672 drivers were screened and 7 were arrested for driving while intoxicated Based on those results we can estimate that P W 0 01042 where W denotes the event of screening a driver and getting someone who is intoxicated What does P W denote and what is its value What does P W represent OA P W denotes the probability of screening a driver and finding that he or she is not intoxicated OB P W denotes the probability of screening a driver and finding that he or she is intoxicated OC P W denotes the probability of a driver passing through the sobriety checkpoint OD P W denotes the probability of driver being intoxicated P W Round to five decimal places as needed

A research center poll showed that 83 of people believe that it is morally wrong to not report all income on tax returns What is the probability that someone does not have this belief The probability that someone does not believe that it is morally wrong to not report all income on tax returns is Type an integer or a decimal

Each of two parents has the genotype red blond which consists of the pair of alleles that determine hair color and each parent contributes one of those allele a child Assume that if the child has at least one red allele that color will dominate and the child s hair color will be red a List the different possible outcomes Assume that these outcomes are equally likely b What is the probability that a child of these parents will have the blond blond genotype c What is the probability that the child will have red hair color a List the possible outcomes OA red blond and blond red B red red and blond blond OC red red red blond blond red and blond blond OD red red red blond and blond blond b The probability that a child of these parents will have the blond blond genotype is Round to two decimal places as needed The probability that the child will have red hair color is

A boat capsized and sank in a lake Based on an assumption of a mean weight of 149 lb the boat was rated to carry 60 passengers so the load limit was 8 940 lb After the boat sank the assumed mean weight for similar boats was changed from 149 lb to 171 lb Complete parts a and b below a Assume that a similar boat is loaded with 60 passengers and assume that the weights of people are normally distributed with a mean of 179 8 lb anc a standard deviation of 39 1 lb Find the probability that the boat is overloaded because the 60 passengers have a mean weight greater than 149 lb The probability is 1 Round to four decimal places as needed b The boat was later rated to carry only 13 passengers and the load limit was changed to 2 223 lb Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 171 so that their total weight is greater than the maximum capacity of 2 223 lb The probability is 0 7915 Round to four decimal places as needed Do the new ratings appear to be safe when the boat is loaded with 13 passengers Choose the correct answer below OA Because there is a high probability of overloading the new ratings do not appear to be safe when the boat is loaded with 13 passengers O B Because the probability of overloading is lower with the new ratings than with the old ratings the new ratings appear to be safe C Because there is a high probability of overloading the new ratings appear to be safe when the boat is loaded with 13 passengers D Because 179 8 is greater than 171 the new ratings do not appear to be safe when the boat is loaded with 13 passengers

An airliner carries 200 passengers and has doors with a height of 74 in Heights of men are normally distributed with a mean of 69 0 in and a standard deviation of 2 8 in Complete parts a through d a If a male passenger is randomly selected find the probability that he can fit through the doorway without bending The probability is 0 9629 Round to four decimal places as needed b If half of the 200 passengers are men find the probability that the mean height of the 100 men is less than 74 in The probability is 0 9999 Round to four decimal places as needed c When considering the comfort and safety of passengers which result is more relevant the probability from part a or the probability from part b Why QA The probability from part a is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height OB The probability from part b is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height OC The probability from part b is more relevant because it shows the proportion of male passengers that will not need to bend D The probability from part a is more relevant because it shows the proportion of male passengers that will not need to bend d When considering the comfort and safety of passengers why are women ignored in this case OA Since men are generally taller than women it is more difficult for them to bend when entering the aircraft Therefore it is more important that men not have to bend than it is important that women not have to bend table propertion of men will necessarily accommodate a greater proportion of women There is no adequate reason to ignore women A separate statistical analysis should be carried out for the case of women

A boat capsized and sank in a lake Based on an assumption of a mean weight of 149 lb the boat was rated to carry 60 passengers so the load limit was 8 940 lb After the boat sank the assumed mean weight for similar boats was changed from 149 lb to 171 lb Complete parts a and b below a Assume that a similar boat is loaded with 60 passengers and assume that the weights of people are normally distributed with a mean of 179 8 lb and a standard deviation of 39 1 lb Find the probability that the boat is overloaded because the 60 passengers have a mean weight greater than 149 lb The probability is 1 Round to four decimal places as needed b The boat was later rated to carry only 13 passengers and the load limit was changed to 2 223 lb Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 171 so that their total weight is greater than the maximum capacity of 2 223 lb The probability is 0 7915 Round to four decimal places as needed Do the new ratings appear to be safe when the boat is loaded with 13 passengers Choose the correct answer below OA Because there is a high probability of overloading the new ratings do not appear to be safe when the boat is loaded with 13 passengers O B Because the probability of overloading is lower with the new ratings than with the old ratings the new ratings appear to be safe OC Because there is a high probability of overloading the new ratings appear to be safe when the boat is loaded with 13 passengers D Because 179 8 is greater than 171 the new ratings do not appear to be safe when the boat is loaded with 13

The ages years of three government officials when they died in office were 56 45 and 60 Complete parts a through d B 56 56 56 45 56 60 45 45 45 60 60 60 C 56 45 56 60 45 60 OD 56 45 56 60 45 56 45 60 60 56 60 45 b Find the range of each of the samples then summarize the sampling distribution of the ranges in the format of a table representing the probability distribution Sample Range Probability 0 4 11 O O O 15 CIB MONONO NO Type an integer or a fraction c Compare the population range to the mean of the sample ranges Choose the correct answer below A The population range is equal to the youngest official at the time of death and the mean of the sample ranges is equal to the oldest official at the time of death B The population range is not equal to the mean of the sample ranges it is also not equal to the age of the oldest official or age of the youngest official at the time of death O C The population range is equal to the age of the oldest official at the time of death and the mean of the sample ranges is equal to the youngest official at the time of death D The population range is equal to the mean of the sample ranges d Do the sample ranges target the value of the population range In general do sample ranges make good estimators of population ranges Why or why not A The sample ranges do not target the population range therefore sample ranges make good estimators of population ranges OB The sample ranges target the population range therefore sample ranges do not make good estimators of population ranges C The sample ranges target the population range therefore sample ranges make good estimators of population ranges t the population range therefore sample ranges do not make good estimators of population ranges

Assume that a randomly selected subject is given a bone density test Those test scores are normally distributed with a mean of 0 and a standard deviation of 1 Find the probability that a given score is less than 0 53 and draw a sketch of the region Sketch the region Choose the correct graph below O A 0 53 OB 0 53 The probability is Round to four decimal places as needed O C 0 53 Q O D 0 53 0 53

What does the notation Za The expression za denotes the z score with an area of a to its left between z and Za

Assume a population of 1 3 and 8 Assume that samples of size n 2 are randomly selected with replacement from the population Listed below are the nine different samples Complete parts a through d below 1 1 a Find the value of the population standard deviation o 1 3 1 8 Round to three decimal places as needed 3 1 OS Type integers or fractions c Find the mean of the sampling distribution of the sample standard deviations The mean of the sampling distribution of the sample standard deviations is Round to three decimal places as needed 3 3 3 8 8 1 b Find the standard deviation of each of the nine samples then summarize the sampling distribution of the standard deviations in the format of a table representing the probability distribution of the distinct standard deviation values Use ascending order of the sample standard deviations S Probability 8 3 8 8 d Do the sample standard deviations target the value of the population standard deviation In general do sample standard deviations make good estimators of population standard deviations why not OA The sample standard deviations do not target the population standard deviation therefore sample standard deviations are biased estimators OB The sample standard deviations do target the population standard deviation therefore sample standard deviations are unbiased estimators The sample standard deviations do target the population standard deviation therefore sample standard deviations are biased estimators doviation therefore sample standard deviations are unbiased estimators

A normal distribution is informally described as a probability distribution that is bell shaped when graphed Draw a rough sketch of a curve having the bell shape that is characteristic of a normal distribution Choose the correct answer below O A B O C O D

Assume the readings on thermometers are normally distributed with a mean of 0 C and a standard deviation of 1 00 C Find the probability that a randomly selected thermometer reads between 1 06 and 0 09 and draw a sketch of the region Click to view page 1 of the table Click to view page 2 of the table Sketch the region Choose the correct graph below O A 1 06 0 09 O B 1 06 0 09 The probability is Round to four decimal places as needed Ly O C 1 06 0 09 Q G

Assume that females have pulse rates that are normally distributed with a mean of 75 0 beats per minute and a standard deviation of o 12 5 beats per minute Complete parts a through c below a If 1 adult female is randomly selected find the probability that her pulse rate is less than 82 beats per minute The probability is Round to four decimal places as needed b If 16 adult females are randomly selected find the probability that they have pulse rates with a mean less than 82 beats per minute The probability is Round to four decimal places as needed c Why can the normal distribution be used in part b even though the sample size does not exceed 30 A Since the distribution is of sample means not individuals the distribution is a normal distribution for any sample size B Since the mean pulse rate exceeds 30 the distribution of sample means is a normal distribution for any sample size OC Since the distribution is of individuals not sample means the distribution is a normal distribution for any sample size OD Since the original population has a normal distribution the distribution of sample means is a normal distribution for any sample size

An airliner carries 200 passengers and has doors with a height of 74 in Heights of men are normally distributed with a mean of 69 0 in and a standard deviation of 2 8 in Complete parts a through d a If a male passenger is randomly selected find the probability that he can fit through the doorway without bending The probability is 0 9629 Round to four decimal places as needed b If half of the 200 passengers are men find the probability that the mean height of the 100 men is less than 74 in The probability is 0 9999 Round to four decimal places as needed c When considering the comfort and safety of passengers which result is more relevant the probability from part a or the probability from part b Why OA The probability from part a is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height OB The probability from part b is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height OC The probability from part b is more relevant because it shows the proportion of male passengers that will not need to bend OD The probability from part a is more relevant because it shows the proportion of male passengers that will not need to bend

When two births are randomly selected the sample space for genders is bb bg gb and gg Assume that those four outcomes are equally likely Construct a table that describes the sampling distribution of the sample proportion of girls from two births Does the mean of the sample proportions equal the proportion of girls in two births Does the result suggest that a sample proportion is an unbiased estimator of a population proportion For the entire population assume the probability of having a boy is the probability of having a girl is and this is not affected by how many boys or girls have previously been born Determine the probabilities of each sample proportion Sample proportion of girls 0 0 5 1 Does the mean of the sample proportions equal the proportion of girls in two births A Yes both the mean the sample proportions and the population proportion are 3 GELER 1 B Yes both the mean of the sample proportions and the population proportion are 2 OC No the mean of the sample proportions and the population proportion are not equal OD Yes both the mean of the sample proportions and the population proportion are 4 Does the result suggest that a sample proportion is an unbiased estimator of a population proportion OA No because the sample proportions and the population proportion are the same OB Yes because the sample proportions and the population proportion are not the same OC No because the sample proportions and the population proportion are not the same OP Yes because the sample proportions and the population proportion are the same Probability 0 25 0 5 0 25 Type integers or simplified fractions

A survey found that women s heights are normally distributed with mean 62 8 in and standard deviation 2 3 in The survey also found that men s heights are normally distributed with mean 69 2 in and standard deviation 3 7 in Most of the live characters employed at an amusement park have height requirements of a minimum of 55 in and a maximum of 64 in Complete parts a and b below a Find the percentage of men meeting the height requirement What does the result suggest about the genders of the people who are employed as characters at the amusement park The percentage of men who meet the height requirement is 7 99 Round to two decimal places as needed Since most men the height requirement it is likely that most of the characters are

When two births are randomly selected the sample space for genders is bb bg gb and gg Assume that those four outcomes are equally likely Construct a table that describes the sampling distribution of the sample proportion of girls from two births Does the mean of the sample proportions equal the proportion of girls in two births Does the result suggest that a sample proportion is an unbiased estimator of a population proportion For the entire population 1 1 the probability of having a girl is assume the probability of having a boy is 2 affected by how many boys or girls have previously been born Determine the probabilities of each sample proportion Sample proportion of girls 0 0 5 1 and this is not 2 Probability 0 25 0 5 0 25 Type integers or simplified fractions Does the mean of the sample proportions equal the proportion of girls in two births 1 3 1 OA Yes both the mean of the sample proportions and the population proportion are OB Yes both the mean of the sample proportions and the population proportion are OC No the mean of the sample proportions and the population proportion are not equal D Yes both the mean of the sample proportions and the population proportion are 2 1

The ages years of three government officials when they died in office were 56 45 and 60 Complete parts a through d a Assuming that 2 of the ages are randomly selected with replacement list the different possible samples A 56 56 56 45 56 60 45 56 45 45 45 60 60 56 60 45 60 60 OB 56 56 56 45 56 60 45 45 45 60 60 60 C 56 45 56 60 45 60 OD 56 45 56 60 45 56 45 60 60 56 60 45 b Find the range of each of the samples then summarize the sampling distribution of the ranges in the format of a table representing the probability distribution Sample Range Probability

The overhead reach distances of adult females are normally distributed with a mean of 195 cm and a standard deviation of 7 8 cm a Find the probability that an individual distance is greater than 208 40 cm b Find the probability that the mean for 20 randomly selected distances is greater than 193 20 cm c Why can the normal distribution be used in part b even though the sample size does not exceed 30 a The probability is 0 0429 Round to four decimal places as needed b The probability is Round to four decimal places as needed

A water taxi carries passengers from harbor to another Assume that weights of passengers are normally distributed with a mean of 184 lb and a standard deviation of 35 lb The water taxi has a stated capacity of 25 passengers and the water taxi was rated for a load limit of 3500 lb Complete parts a through d below a Given that the water taxi was rated for a load limit of 3500 lb what is the maximum mean weight of the passengers if the water taxi is filled to the stated capacity of 25 passengers The maximum mean weight is 140 lb Type an integer or a decimal Do not round b If the water taxi is filled with 25 randomly selected passengers what is the probability that their mean weight exceeds the value from part a The probability is Round to four decimal places as needed

An airliner carries 200 passengers and has doors with a height of 74 in Heights of men are normally distributed with a mean of 69 0 in and a standard deviation of 2 8 in Complete parts a through d a If a male passenger is randomly selected find the probability that he can fit through the doorway without bending The probability is Round to four decimal places as needed

For bone density scores that are normally distributed with a mean of 0 and a standard deviatic of 1 find the percentage of scores that are a significantly high or at least 2 standard deviations above the mean b significantly low or at least 2 standard deviations below the mean c not significant or less than 2 standard deviations away from the mean a The percentage of bone density scores that are significantly high is Round to two decimal places as needed

When women were finally allowed to become pilots of fighter jets engineers needed to redesign the ejection seats because they had been originally designed for men only The ejection seats were designed for men weighing between 140 lb and 211 lb Weights of women are now normally distributed with a mean of 167 lb and a standard deviation of 45 lb Complete parts a through c below a If 1 woman is randomly selected find the probability that her weight is between 140 lb and 211 lb The probability is approximately Round to four decimal places as needed

When two births are randomly selected the sample space for genders is bb bg gb and gg Assume that those four outcomes are equally likely Construct a table that describes the sampling distribution of the sample proportion of girls from two births Does the mean of the sample proportions equal the proportion of girls in two births Does the result suggest that a sample proportion is an unbiased estimator of a population proportion For the entire population 1 1 assume the probability of having a boy is the probability of having a girl is and this is not affected by how many boys or girls have previously been born Determine the probabilities of each sample proportion Sample proportion of girls Probability ors or simplified fractions

A boat capsized and sank in a lake Based on an assumption of a mean weight of 149 lb the boat was rated to carry 60 passengers so the load limit was 8 940 lb After the boat sank the assumed mean weight for similar boats was changed from 149 lb to 171 lb Complete parts a and b below a Assume that a similar boat is loaded with 60 passengers and assume that the weights of people are normally distributed with a mean of 179 8 lb and a standard deviation of 39 1 lb Find the probability that the boat is overloaded because the 60 passengers have a mean weight greater than 149 lb The probability is Round to four decimal places as needed