Probability Questions and Answers

33 When playing roulette at a casino a gambler is trying to decide whether to bet 20 on the number 15 or to bet 20 that the outcome is any one of the five possibilities 00 0 1 2 or 3 The gambler 38 knows that the expected value of the 20 bet for a single number is 1 05 For the 20 bet that the outcome is 00 0 1 2 or 3 there is a probability of of making a net profit of 100 and a probability of losing 20 38 a Find the expected value for the 20 bet that the outcome is 00 0 1 2 or 3 b Which bet is better a 20 bet on the number 15 or a 20 bet that the outcome is any one of the numbers 00 0 1 2 or 3 Why a The expected value is Round to the nearest cent as needed b Since the expected value of the bet on the number 15 is COCOS than the expected value for the bet that the outcome is 00 0 1 2 or 3 the bet on is better

Multiple choice questions each have four possible answers a b c d one of which is correct Assume that you guess the answers to three such questions a Use the multiplication rule to find P WWC where C denotes a correct answer and W denotes a wrong answer P WWC Type an exact answer b Beginning with WWC make a complete list of the different possible arrangements of one correct answer and two wrong answers then find the probability for each entry in the list P WWC see above P WCW P CWW Type exact answers c Based on the preceding results what is the probability of getting exactly one correct answer when three guesses are made Type an exact answer

11 Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2800 grams and a standard deviation of 700 grams while babies born after a gestation period of 40 weeks have a mean weight of 3200 grams and a standard deviation of 530 grams If a 34 wee gestation period baby weighs 2400 grams and a 41 week gestation period baby weighs 2800 grams find the corresponding z scores Which baby weighs less relative to the gestation period Find the corresponding z scores Which baby weighs relatively less Select the correct choice below and fill in the answer boxes to complete your choice Round to two decimal places as needed OA The baby born in week 41 weighs relatively less since its z score for the baby born in week 34 the z score of OB The baby born in week 41 weighs relatively less since its z score the z score of for the baby born in week 34 OC The baby born in week 34 weighs relatively less since its z score the z score of for the baby born in week 41 OD The baby born in week 34 weighs relatively less since its z score is smaller than is larger than is smaller than is larger than

y was conducted that asked 1003 people how many books they had read in the indicated that x 12 8 books and s 16 6 books Construct a 90 confidence an number of books neople read Interpret the interval If repeated samples are taken 90 of them will have a sample mean between There is a 90 probability that the true mean number of books read is between There is 90 confidence that the population mean number of books read is bet and

A university conducted a survey of 383 undergraduate students regarding satisfaction with student government Results of the survey are shown in the table by class rank Complete parts a through d below Satisfied Neutral Not satisfied Total Freshman 60 28 16 104 Sophomore 46 19 21 86 a If a survey participant is selected at random what is the probability that he or she is satisfied with student government P satisfied Round to three decimal places as needed b If a survey participant is selected at random what is the probability that he or she is a junior P junior Round to three decimal places as needed P satisfied and junior Round to three decimal places as needed P satisfied or junior Reuss Junior Senior 67 60 10 15 19 96 c If a survey participant is selected at random what is the probability that he or she is satisfied and a junior 22 97 mal pla d If a survey participant is selected at random what is the probability that he or she is satisfied or a junior pooded Y Total 233 72 78 383

dents who first enrolled in two year public institutions in a recent semester the ned a bachelor s degree within six years was 0 387 The president of a certain believes that the proportion of students who enroll in her institution have a hig tion rate tegers or decimals Do not round at would it mean to make a Type Il error the hypothesis that the proportion of students who earn when in fact the proportion esident lor s degree within six years is ntegers or decimals Do not round

se a simple random sample of size n 150 is obtained from a population whose size 000 and whose population proportion with a specified characteristic is p 0 8 Compl through c below at is the probability of obtaining x 126 or more individuals with the characteristic The P p 0 84 84 Round to four decimal places as needed at is the probability of obtaining x 111 or fewer individuals with the characteristic The P p 0 74 74 Round to four decimal places as needed

The data show the number of vacation days used by a sample of 20 employees in a recent year Use technology to answer parts a and b a Find the data set s first second and third quartiles b Draw a box and whisker plot that represents the data set 10 399 39 1 9 8 7 7 3 6 0 8 8 3 5 390 a Find the three quartiles Q Q Q3 Type integers or decimals Do not round b Choose the correct answer plot below Note that different technologies will produce slightly different results O A 3 co 6 O 9 OB 0 3 6 9 O C

ording to a study done by Nick Wilson of Otago University Wellington the probability a domly selected individual will not cover his or her mouth when sneezing is 0 267 Suppose on a bench in a mall and observe people s habits as they sneeze Complete parts a Using the binomial distribution what is the probability that among 12 randomly erved individuals fewer than 5 do not cover their mouth when sneezing probability is und to four decimal places as needed Using the binomial distribution would you be surprised if after observing 12 individuals fe half covered their mouth when sneezing Why be surprising because the probability is which is it 0 0

hine whether the scatter diagram indicates inear relation may exist between the two es If the relation is linear determine er it indicates a positive or negative ation between the variables s information to answer the following two variables nave a linear relationship The data points have a linear relationship because they lie mainly in a straight line The data points have a linear relationship because they do not lie Response 30 20 10 04 OB 20 Explanatory 40 ha The data points do relationship because they mainly in a straight line D The data points do not ha relationship because they

greater than less than or approximately equal to the median 10 Justify your answer 8 6 4 A x M because the histogram is symmetric OC x M because the histogram is skewed right E X M because the histogram is B x M because the histogram skewed left OD x M because the histogram skewed right F x M because the histogram

A simple random sample of size n 200 drivers with a valid driver s license is asked if they drive an American made automobile Of the 200 drivers surveyed 110 responded that they drive an American made automobile Determine if a majority of those with a valid driver s license drive an American made automobile at the a 0 05 level of significance Which distribution should be used for this hypothesis test OA The Student s t distribution because the parameter is the mean o is not known and the model conditions are satisfied OB The chi square distribution because the parameter is o or o and the model conditions are satisfied OC The normal distribution because the parameter is a proportion p and the model conditions are satisfied O D The normal distribution because the parameter is the mean o is known and the model

A group of adult males has foot lengths with a mean of 27 17 cm and a standard deviation of 1 39 cm Use the range rule of thumb for identifying significant values to identify the limits separating values that are significantly low or significantly high Is the adult male foot length of 30 3 cm significantly low or significantly high Explain Type an integer or a decimal Do not round Select the correct choice below and fill in the answer box es to complete your choice The adult male foot length of 30 3 cm is significantly high because it is greater than Type an integer or a decimal Do not round OA OB CITE C The adult male foot length of 30 3 cm is significantly low because it is less than Type an integer or a decimal Do not round The adult male foot length of 30 3 cm is not significant because it is between Type integers or decimals Do not round cm cm cm and cm

20 A golf association requires that golf balls have a diameter that is 1 68 inches To determine if golf balls conform to the standard a random sample of golf balls was selected Their diameters are shown in the accompanying data table Do the golf balls conform to the standards Use the x 0 01 level of significance Golf Ball Diameter inches 1 683 1 686 1 684 1 685 1 676 1 677 1 685 1 682 What can be concluded from the hypothesis test 1 682 1 685 1 673 1 674 O A Do not reject Ho There is sufficient evidence to conclude that the golf balls do not conform to the association s standards at the x 0 01 level of significance OB Reject Ho There is not sufficient evidence to conclude that the golf balls do not conform to the association s standards at the a 0 01 level of significance OC Do not reject Ho There is not sufficient evidence to conclude that the golf balls do not conform to the association s standards at the a 0 01 level of significance O D Reject Ho There is sufficient evidence to conclude that the golf balls do not conform to the association s standards at the x 0 01 level of significance

Use the same scales to construct modified boxplots for the pulse rates of men and women from the accompanying data sets Identify any outliers Use the boxplots to compare the two data sets Click the icon to view the data sets OC H8 40 50 60 70 80 90 100110 xx AENEAN Q G Q GEIXE OD 40 50 60 70 80 90 100110 10 50 60 70 69 65 1 Q G Q Q

opulation that is known to be normally distributed Answer parts a d C Draw a t distribution that depicts the critical region s Which of the following grap ritical region s in the t distribution A Q B Q O C

In a clinical trial 17 out of 827 patients taking a prescription drug daily complained symptoms Suppose that it is known that 1 7 of patients taking competing drugs flulike symptoms Is there sufficient evidence to conclude that more than 1 7 of t experience flulike symptoms as a side effect at the a 0 01 level of significance What are the null and alternative hypotheses Ho versus H Type integers or decimals Do not round

17 In a clinical trial 17 out of 827 patients taking a prescription drug daily complained of flulike symptoms Suppose that it is known that 1 7 of patients taking competing drugs complain of flulike symptoms Is there sufficient evidence to conclude that more than 1 7 of this drug s users experience flulike symptoms as a side effect at the x 0 01 level of significance Choose the correct conclusion below O A Since P value x reject the null hypothesis and conclude that there is sufficient evidence that more than 1 7 of the users experience flulike symptoms OB Since P value x do not reject the null hypothesis and conclude that there is not sufficient evidence that more than 1 7 of the users experience flulike symptoms OC Since P value a do not reject the null hypothesis and conclude that there is sufficient evidence that more than 1 7 of the users experience flulike symptoms O D Since P value a reject the null hypothesis and conclude that there is not sufficient evidence that more than 1 7 of the users experience flulike symptoms

a clinical trial 17 out of 827 patients taking a prescription drug daily complained mptoms Suppose that it is known that 1 7 of patients taking competing drugs ke symptoms Is there sufficient evidence to conclude that more than 1 7 of t serience flulike symptoms as a side effect at the a 0 01 level of significance ed the test statistic Zo Round to two decimal places as needed d the P value alue Round to three decimal places as needed

15 Three years ago the mean price of an existing single family home was 243 713 A real estate broker believes that existing home prices in her neighborhood are lower a State the null and alternative hypotheses in words b State the null and alternative hypotheses symbolically c Explain what it would mean to make a Type I error d Explain what it would mean to make a Type Il error State the alternative hypothesis in words Choose the correct answer below OA The mean price of a single family home in the broker s neighborhood is less than 243 713 OB The mean price of a single family home in the broker s neighborhood is different from 243 713 OC The mean price of a single family home in the broker s neighborhood is 243 713 O D The mean price of a single family home in any neighborhood is 243 713

Construct a 90 confidence interval of the population proportion using the given information x 40 n 200 Level of Confidence 1 a 100 90 95 99 The lower bound is Area in Each Tail 0 05 0 025 0 005 2 The upper bound is Round to three decimal places as needed Critical Value z 1 645 1 96 2 575

ee years ago the mean price of an existing single family home was 24 Ker believes that existing home prices in her neighborhood are lower State the nuli nypotnesis in words Cnoose the correct answer Delow A The mean price of a single family home in the broker s neighborhood is less than 243 713 B The mean price of a single family home in any neighborhood is 243 713 C The mean price of a single family home in the broker s neighborhood is 243 713 D The mean price of a single family home in the broker s neighborhood is different 243 713

ples have mean absolute deviations that do not center about the value of the mean absolute deviation of the population What does this ind how that when samples of size 2 are randomly selected about a sample mean absolute deviation being used as an estimator of the mean absolute deviation of a population as a bit oluts are avul a sampit man att vian ay mae as a coma un ie man i a po A The sample mean absolute deviation is a biased estimator of the population mean absolute deviation because the sample statistic centers around a different va than the population parameter OB The sample mean absolute deviation is a biased estimator of the population mean absolute deviation because the sample statistic centers around the mean valu the population OC The sample mean absolute deviation is an unbiased estimator of the population mean absolute deviation because the sample statistic centers around the mean value of the population ulation abcoluto

is left tailed right tailed or two tailed What parameter is being tested Ho H 3 H 3 What type of test is being conducted in this problem Two tailed test O Right tailed test

he null and alternative hypotheses are given Determine whether the hyp left tailed right tailed or two tailed What parameter is being tested Ho 3 H 3 What parameter is being tested O Population standard deviation O Population mean Population proportion

sample standard deviation s is found to be 4 9 d If the sample size is 18 what conditions must be satisfied to compute the confidence OA The sample size must be large and the sample should not have any outliers OB The sample must come from a population that is normally distributed and the sar size must be large OC The sample data must come from a population that is normally distributed with ne outliers

6 In a survey of 2065 adults in a certain country conducted during a period of economic uncertainty 66 thought that wages paid to workers in industry were too low The margin of error was 4 percentage points with 95 confidence For parts a through d below which represent a reasonable interpretation of the survey results For those that are not reasonable explain the flaw c We are 95 confident that the interval from 0 62 to 0 70 contains the true proportion of adults in the country during the period of economic uncertainty who believed wages paid to workers in industry were too low Is the interpretation reasonable O A The interpretation is reasonable OB The interpretation is flawed The interpretation provides no interval about the population proportion OC The interpretation is flawed The interpretation indicates that the level of confidence is varying OD The interpretation is flawed The interpretation suggests that this interval sets the standard for all the other intervals which is not true

Listed below are the amounts dollars it costs for marriage proposal packages at different baseball stadiums Find the range variance and standard deviation for the given sample data Include appropriate units in the results Are there any outliers and are they likely to have much of an effect on the measures of variation 37 50 50 65 70 90 90 120 195 209 250 350 500 2000 2500 KOUNG WO ne decam pace as heeveu Are there any outliers and if so are they likely to have much of an effect on the measures of variation OA Yes the largest amounts are much higher than the rest of the data and appear to be outliers It is likely that these are having a large effect on the measures of variation OB Yes the largest amounts are much higher than the rest of the data and appear to be outliers It is not likely that these are having a large effect on the measures of variation OC Yes the smallest amounts are much lower than the rest of the data and appear to be outliers It is not likely that these are having a large effect on the measures of variation OD No there are not any outliers

ermine the point estimate of the population proportion the margin of error for the f fidence interval and the number of individuals in the sample with the specified cha or the sample size provided Lower bound 0 489 upper bound 0 761 n 1200 una to the nearest nousanain as needed margin of error is und to the nearest thousandth as needed number of individuals in the sample with the specified characteristic is und to the nearest integer as needed

A simple random sample of size n 19 is drawn from a population that is normally distributed The sample mean is found to be x 64 anc the sample standard deviation is found to be s 20 Construct a 90 confidence interval about the population mean The lower bound is 56 06 The upper bound is 71 94 Round to two decimal places as needed

In a survey of 1006 adults a polling agency asked When you retire do you think you will have enough money to live comfortably or no Of the 1006 surveyed 532 stated that they were worried about having enough money to live comfortably in retirement Construct a 95 confidence interval for the proportion of adults who are worried about having enough money to live comfortably in retirement Click here to view the standard normal distribution table page 1 Click here to view the standard normal distribution table page 2 Click here to view the table of critical t values Click here to view the table of critical values of the chi square distribution Select the correct choice below and fill in the answer boxes to complete your choice Use ascending order Round to three decimal places as needed OA There is a 95 probability that the true proportion of worried adults is between B There is 95 confidence that the true proportion of worried adults is between OC 95 of the population lies in the interval between and and and

35 A factory have two production lines produces certain goods The newer production line produces 90 of all goods with a defection rate of 3 the other have a defective rate of 5 What is the overall defective rate in the factory If a product is found defective what is the chance that it was produced by the newer production line

3 15 There are two container of Marbles Container A has 20 black and 30 white marbles and Container B has 300 white and 100 black marbles One person randomly sect a marble from container A and put it into B now you will randomly choose 5 marbles from container B what is the chance that exactly two are white

According to a recent Pew Research poll 67 of Americans say that the U S economic system favors the powerful In a recent sample of 290 Americans 245 agreed that the U S economic system unfairly favors the powerful Determine the values of p and p Round solutions to two decimal places if necessary P

A presidential candidate plans to begin her campaign by visiting the capitals in 4 of 46 states What is the probability that she selects the route of four specific capitals P she selects the route of four specific capitals Type an integer or a simplified fraction

A student wants to simulate 44 birthdays but she does not have a calculator or software program available so she makes up 44 numbers between 1 and 365 Is it okay to conduct the simulation this way Why or why not Choose the correct answer below OA Yes People are capable of randomly making up numbers between two values OB Yes People are better at picking birth dates than computers since they can base the numbers on the birth dates of people they know OC No Simulations must be performed with either a calculator or a statistical program OD No People generally favor some numbers over others so that they don t select numbers with a process that is truly random

You are given that sin A your answer as a fraction 1 25 H with A in Quadrant IV and cos B with B in Quadrant III Find sin A B Give

A survey was conducted that asked 1013 people how many books they had read in the past year Results indicated that x 10 4 books and s 16 6 books Construct a 90 confidence interval for the mean number of books people read Interpret the interval Click the icon to view the table of critical t values Construct a 90 confidence interval for the mean number of books people read and interpret the result Select the correct choice below and fill in the answer boxes to complete your choice Use ascending order Round to two decimal places as needed A There is a 90 probability that the true mean number of books read is between and OB There is 90 confidence that the population mean number of books read is between OC If repeated samples are taken 90 of them will have a sample mean between and and

Find the indicated probability Round to the nearest thousandth 16 A sample of 4 different calculators is randomly selected from a group containing 18 that are defective and 40 that ha no defects What is the probability that at least one of the calculators is defective 16

18 18 A state lottery involves the random selection of six different numbers between 1 and 31 If you select one six number combination what is the probability that it will be the winning combination

Find the indicated probability Express your answer as a simplified fraction unless otherwise noted 15 The following table contains data from a study of two airlines which fly to Small Town USA 3 Podunk Airlines Upstate Airlines Number of flights Number of flights which were on time which were late 33 43 6 5

10 The table below describes the smoking habits of a group of asthma sufferers Men Women Nonsmoker 433 408 Occasional Regular smoker smoker 66 70 50 31 2 Heavy smoker Total 34 35 583 514

11 A bag contains 6 red marbles 3 blue marbles and 1 green marble Find P not blue

A IRS auditor randomly selects 3 tax returns from 45 returns of which 15 contain errors What is the probability that she elects none of those containing errors Round to four decimal places 9

The mean gas mileage for a hybrid car is 57 miles per gallon Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3 5 miles per gallon a What proportion of hybrids gets over 60 miles per gallon b What proportion of hybrids gets 51 miles per gallon or less c What proportion of hybrids gets betwee 57 and 61 miles per gallon d What is the probability that a randomly selected hybrid gets less than 45 miles per gallon Click the icon to view a table of areas under the normal curve a The proportion of hybrids that gets over 60 miles per gallon is Round to four decimal places as needed

The mean incubation time of fertilized eggs is 22 days Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day a Determine the 19th percentile for incubation times b Determine the incubation times that make up the middle 39 Click the icon to view a table of areas under the normal curve a The 19th percentile for incubation times is days Round to the nearest whole number as needed

possible for their children to have brown eyes probability 0 75 blue eyes 0 125 or green eyes 0 125 a What is the probability the rst blue eyed child they have is their third child Assume that the eye colors of the children are independent of each other b If they have six children what is the probability that exactly two will have green eyes c If they have six children what is the probability that at least one will have green eyes

Aubrey buys a bag of cookies that contains 7 chocolate chip cookies 9 peanut butter cookies 5 sugar cookies and 8 oatmeal raisin cookies What is the probability that Aubrey randomly selects a peanut butter cookie from the bag eats it then randomly selects another peanut butter cookie Express your answer as a reduced fraction

A very skilled court stenographer makes one typographical error typo per hour on average a What probability distribution is most appropriate for calculating the probability of a given number of typos this stenographer makes in an hour O Poisson O binomial O negative binomial geometric b What are the mean and the standard deviation of the number of typos this stenographer makes Enter your answers as whole numbers 1 1 mean standard deviation c Would it be considered unusual if this stenographer made 5 typos in a given hour Making 5 typos in a given hour is more than two standard deviations above the mean so it would T be unusual d Calculate the probability that this stenographer makes at most 5 typos in a given hour Round your answer to four decimal places

WorkoutHours TVHours StressLevel Pearson Correlation Sig 2 tailed N Pearson Correlation Sig 2 tailed N Pearson Correlation Sig 2 tailed N 1 40 233 149 40 428 006 40 233 149 40 1 40 053 745 40 428 006 40 053 745 40 1 40 Correlation is significant at the 0 01 level 2 tailed 10 Based on the above Correlation table which correlations are significant