Statistics Questions

10 pes We bought a pack of 10 lightbulbs from a garage sale and o of them don t work If we were to collect a random sample of 2 lightbulbs no replacement and count the number of lightbulbs that are defective create a probability distribution for this discrete random variable a First define your random variable X The random variable X will be defined as the number of defective lightbulbs in a random sample of 2 lightbulbs chosen without replacement from the pack of 10 bulbs X can take from values 0 to 2 where X 0 means both bulbs are working X 1 means one bulbs is working and X 2 means both bulbs are defective b Next showing work for all of your probabilities in the space below fill in the table below round probabilities to 4 decimal places X P X total of bulbs 10 of defective bulbs 6 of working bulbs 4 probability of 2 bulbs working 4c 100 c What do the probabilities sum up to 70 1333 bc 4c 0 53332 probability of 1 bulbs working IPC 6c probability of 2 bulbs working 10 0 3333 1 0 1333 0 5333 0 3333

5 In an Oreo factory the mean mass of a cookie is given as 40 g For quality control the standard deviation is 2 g a If 10 000 cookies were produced how many cookies are within 5 g of the mean b Cookies are rejected if they weigh more than 44 g or less than 36 g How many cookies would you expect to be rejected in a sample of 10 000 cookies

6 The speeds of cars on the highway have a mean of 95 km h with a standard deviation of 5 km h a What percentage of cars averaged less than 83 km h b If a police car stopped cars that were going more than 104 km h how many cars would they stop if there wer 8000 cars on the highway

The ability to find a job after graduation is very important to GSU students as it is to the students at most colleges and universities Suppose we take a poll random sample of 3870 students classified as Juniors and find that 3234 of them believe that they will find a job immediately after graduation Find the 90 confidence interval for the proportion of GSU Juniors who believe that they will immediately be employed after graduation Use Z1 645 Use the unrounded values in Excel to find the answers to 2 3 and 4 1 Find the sample proportion of GSU Juniors who believe that they will immediately be employed after graduation Fill in the blanks by selecting one option from each menu aby Part 1 3 points aby Part 2 3 points aby Part 3 3 points aby Part 4 3 points aby Part 5 3 points 15 points 2 The standard error for sample proportion has a value of 3 The margin of error has a value of 4 Find the 90 confidence interval for GSU Juniors who believe that they will immediately be employed after graduation

Parking survey For a class assignment a group of statistics students set up a table near the 10 points student parking lot They asked students who passed by to complete a quick survey about whether they support the building of a multi level parking structure that would add 425 new spaces at the college A B C ENTER They used the information from the survey to calculate the 95 confidence interval 0 53 0 72 To which population does the confidence interval apply D Select one answer They apply to all students at the college They apply only to the population of those who use the student parking lot The results do not apply to any population because this was a convenience sample They apply only to the population of those students who drive to the college

A Gallup survey of 2326 adults at least 18 years old in the U S found that 419 of them have donated blood in the past two years Construct a 99 confidence interval for the population proportion of adults in the U S who have donated blood in the past two years Round your answer to three decimal places Use Z 2 576 Use the unrounded values in Excel to find the answers to 2 3 and 4 1 Find the sample proportion of adults in the U S who have donated blood in the past two years Round your answer to three decimal places 2 The standard error for sample proportion has a value of 3 The margin of error has a value of 4 Construct the 99 confidence interval for adults who have donated blood in the past two years Fill in the blanks by selecting one option from each menu aby Part 1 3 points aby Part 2 3 points aby Part 3 3 points aby Part 4 3 points ab Part 5 3 points 15 points C

A machine is designed to fill 16 ounce bottles of shampoo When the machine is working properly the amount poured into the bottles follows a normal distribution with mean 16 05 ounces with a standard deviation of 3005 ounces If four bottles are randomly selected each hour and the number of ounces in each bottle is measured then 95 of the means calculated should occur in what interval Type numbers in the boxes aby Part 1 5 points aby Part 2 5 points 10 points Hint the standard deviation rule says that 95 of the observations are within how many standard deviations away from the mean Round answers to four decimal places

Suppose that the distribution for total amounts spent by students vacationing for a week in Florida is normally distributed with a mean of 650 and a standard deviation of 120 Suppose you take a simple random sample SRS of 5 students from this distribution Type numbers in the boxes 10 points What is the probability that a SRS of 5 students will spend an average of between 600 and 700 dollars Round to five decimal places

Type numbers in the boxes 10 points A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5 to 6 with the additional revenue going to education Let p denote the proportion in the sample who say they support the increase Suppose that 4 of all adults in Ohio support the increase The standard deviation of the sampling distribution is Round your answer to four decimal places

Select the correct answer As part of a class project a university student surveyed the students in the cafeteria lunch line to look for a relationship between eye color and ha color among students The table below contains the results of the survey Eye Color Hair Color Blue Gray Green Blond 42 5 21 Red 19 Brown 12 Black 11 Marginal Totals 229 12 25 85 35 OA 0 07 3 B 0 12 63 Brown 10 12 34 64 120 Marginal Totals 78 65 73 87 From the sample population of students with gray eyes what is the relative frequency of students with red hair 303

In Australia in 1995 of the 2907 indigenous people in prison 17 of them died In that same year of the 14501 non indigenous people in prison 42 of them died Aboriginal deaths in 2013 a Find the probability that an indigenous person in prison dies Enter your answer as a fraction Enter your answer rounded to 3 decimal places b Find the probability that a non indigenous person in prison dies Enter your answer as a fraction Enter your answer rounded to 3 decimal places

12 Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y f x y Jxe x20 and y 0 0 otherwise a What is the probability that the lifetime X of the first component exceeds 3 AUX b What are the marginal pdf s of X and Y Are the two lifetimes independent Explain c What is the probability that the lifetime of at least one component exceeds 3

27 Annie and Alvie have agreed to meet for lunch between noon 0 00 P M and 1 00 PM Denote Annie s arrival time by X Alvie s by Y and suppose X and Y are inde pendent with pdf s 1 x Sy y 3r 0 x 1 0 otherwise 2y 0sys1 0 therwise

Solve for v 4 v13 8 V MEN

A random sample of 310 car buyers was asked about the reason that they chose the car that they did The results are given in the table below Reason for Choosing a Car Freq safety 87 reliability 64 cost 50 38 comfort 47 looks 24 Give your answer rounded to three decimal places performance Find the probability that a randomly selected car buyer will be in the category cost Give your answer as a fraction

Eyeglassomatic manufactures eyeglasses for different retailers They test to see how many defective lenses they made in the time period of January 1 to March 31 A sample of 12571 pairs of lenses were inspected The table below gives the defect and the number of pairs of lenses with that defect Defect type scratch wrong shape spots and bubbles wrong axis wrong height wrong PD Freq 5812 1414 Give your answer rounded to three decimal places 994 1881 1128 1342 Find the probability that a randomly selected a pair of defective lenses will be in the category wrong PD Give your answer as a fraction

A person in a casino decides to play 3 games of blackjack Let W denote a win and L denote a loss Define the event A as the person wins at least one game of blackjack What are the possible outcomes for this event O W LW LLW Ow ww www O www WWL WLW WLL LWW LWL LLW LLL O www WWL WLW WLL LWW LWL LLW O WWL LWL LLW

5 Let X denote the number of Canon SLR cameras sold during a particular week by a certain store The pmf of X is 0 1 1 2 2 Px x 25 15 Sixty percent of all customers who purchase these cameras also buy an extended warranty Let Y denote the number of purchasers during this week who buy an extended warranty 3 3 4 a What is P X 4 Y 2 Hint This probability equals P Y 2 X 4 P X 4 now think of the four purchases as four trials of a binomial experiment with success on a trial corresponding to buying an extended warranty Calculate P X Y b c Determine the joint pmf of X and Y and then the marginal pmf of Y

A family plans to have 3 children For each birth assume that the probability of a boy is the same as the probability of a girl What is the probability that they will have at least one boy and at least one girl 0 0 5 O 0 125 O 0 75 O 0 875 O None of these

A person in a casino decides to play blackjack until he wins a game but he will not play more than 3 games Let W denote a win and L denote a loss What is the sample space for this random experiment Os W LW LLW LLL Os www WWL WLW WLL LWW LWL LLW LLL Os W LW LLW OS W WL WWL WWW Os w ww WWW dort to forum

2 A large but sparsely populated county has two small hospitals one at the south end of the county and the other at the north end The south hospital s emergency room has four beds whereas the north hospital s emer gency room has only three beds Let X denote the num ber of south beds occupied at a particular time on a given day and let y denote the number of north beds occupied at the same time on the same day Suppose that these two rv s are independent that the pmf of X puts probability masses 1 2 3 2 and 2 on the x values 0 1 2 3 and 4 respectively and that the pmf of Y distributes probabilities 1 3 4 and 2 on the y values 0 1 2 and 3 respectively a Display the joint pmf of X and Y in a joint probabil ity table b Compute P X 1 and Y 1 by adding probabilities from the joint pmf and verify that this equals the product of P XS 1 and P Y 1 c Express the event that the total number of beds occu pied at the two hospitals combined is at most 1 in terms of X and Y and then calculate this probability d What is the probability that at least one of the two hospitals has no beds occupied

6 A ski rental shop collected data on the number of rentals on each of ten consecutive Saturdays 44 50 38 96 42 47 40 39 46 50 a Find the mean number and standard deviation of the skis rented b Find the five number summary of the number of skis rented c Find the IQR for these data d Find the lower and upper outlier fences for these data e List any outliers or write NONE if there aren t any

Should the mean median or mode be use to find the center of this distribution Frequency 35 30 25 5 0 P 2 3 4 5 6 7

2 Below are the monthly average temperatures for two cities in the United States Which city would you expect to have the smaller standard deviation Explain why Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec St Louis 29 9 33 9 45 1 56 7 66 1 75 4 79 8 77 6 70 2 58 4 46 2 33 9 San 51 1 54 4 54 9 56 0 56 6 58 4 59 1 60 1 62 3 62 0 57 2 51 7 Francisco

3 Insert the correct symbol in the space provided between the two numbers 25 15

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 Age 15 19 20 24 25 29 30 34 35 39 40 44 45 54 Number of Multiple Births 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 P at least 40 Type an integer or decimal rounded to three decimal places as needed 92 505 1630 2832 1847 379 117 Interpret this result Select the correct choice below and fill in the answer box to complete your choice Type a whole number OA If 1000 multiple births for women 15 54 years old were randomly selected exactly of them would involve a mother who was at least 40 years old OB If 1000 multiple births for women 15 54 years old were randomly selected we would expect about of them to involve a mother who was at least 40 years old an s a 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 a 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 Yes because the probability of a multiple birth involving a mother who was a

Determine whether the events E and F are independent or dependent Justify your answer a E A person living at least 70 years F The same person regularly handling venomous snakes OA E and F are dependent because living at least 70 years has no effect on the probability of a person regularly handling venomous snakes OB E and F are independent because regularly handling venomous snakes has no effect on the probability of a person living at least 70 years OC E and F are dependent because regularly handling venomous snakes can affect the probability of a person living at least 70 years OD E and F are independent because living at least 70 years has no effect on the probability of a person regularly handling venomous snakes b E A randomly selected person coloring her hair black F A different randomly selected person coloring her hair blond OA E can affect the probability of F even if the two people are randomly selected so the events are dependent OB E can affect the probability of F because the people were randomly selected so the events are dependent OC E cannot affect F because person 1 coloring her hair black could never occur so the events are neither dependent nor independent OD E cannot affect F and vice versa because the people were randomly selected so the events are independent

Fill out the following table 4 4 44 45 46 47

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 Age 15 19 20 24 25 29 30 34 35 39 40 44 45 54 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 30 to 39 Type an integer or decimal rounded to three decimal places as needed 92 505 1630 2832 1847 379 117 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 P not 30 to 39 Type an integer or decimal rounded to three decimal places as needed 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 P less than 45 Type an integer or decimal rounded to three decimal places as needed d Determine the probability that a randomly selected multiple birth for women 15 5 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 involved a mother who was at least 40 years old P at least 40 Type an integer or decimal rounded to three decimal places as needed

The probability that a randomly selected 2 year old male garter snake will live to be 3 years old is 0 96263 a What is the probability that two randomly selected 2 year old male garter snakes will live to be 3 years old b What is the probability that eight randomly selected 2 year old male garter snakes will live to be 3 years old c What is the probability that at least one of eight randomly selected 2 year old male garter snakes will not live to be 3 years old Would it be unusual if at least one of eight randomly selected 2 year old male garter snakes did not live to be 3 years old a The probability that two randomly selected 2 year old male garter snakes will live to be 3 years old is Round to five decimal places as needed b The probability that eight randomly selected 2 year old male garter snakes will live be 3 years old is Round to five decimal places as needed c The probability that at least one of eight randomly selected 2 year old male garter snakes will not live to be 3 years old is Round to five decimal places as needed Would it be unusual if at least one of eight randomly selected 2 year old male garter snakes did not live to be 3 years old because the probability of this happening is 0 05

Use the order of operations to simplfy each expression Part 1 62 Part 2 6 Part 3 6

Evaluating Exponents and Notation Complete the table below Use the given expressions to guide your work Notes Use the key shift 6 to make an exponent Example 6 2 gives 6 Use for multiplication Example 6 6 gives 6 6 Exponent form Expanded Form 9 6 6 6 2 2 2 2 Evaluate

Compute the exact values 1 4

Evaluate 10

A survey of 600 randomly selected high school students determined that 536 play organized sports a What is the probability that a randomly selected high school student plays organized sports b Interpret this probability a The probability that a randomly selected high school student plays organized sports is Round to the nearest thousandth as needed b Choose the correct answer below Type a whole number OA If 1 000 high school students were sampled it would be expected that about of them play organized sports OB If 1 000 high school students were sampled it would be expected that exactly of them play organized sports

Evaluate 3

Find the value of 83

Evaluate 24

Evaluate 53

Write 5 5 in exponential form 025 0 55 05 2 05

Write 7 7 7 7 7 7 in exponential notation Ilse to create an oxponent

In a national survey college students were asked How often do you wear a seat belt when riding in a car driven by someone else The response frequencies appear in the table to the right a Construct a probability model for seat belt use by a passenger b Would you consider it unusual to find a college student who never wears a seat belt when riding in a car driven by someone else a Complete the table below Response Never Rarely Sometimes Most of the time Always possible Probability Response Never Rarely Sometimes Most of the time Always Frequency 100 324 600 1038 2284 Round to the nearest thousandth as needed Round to the nearest thousandth as needed Round to the nearest thousandth as needed Round to the nearest thousandth as needed Round to the nearest thousandth as needed b Would you consider it unusual to find a college student who never wears a seat belt when riding in a car driven by someone else OA Yes because 0 01 P never 0 10 OB No because there were 100 people in the survey who said they never wear their seat belt OC No because the probability of an unusual event is 0

a Find the probability that all three have type B blood The probability that all three have type B blood is Round to six decimal places as needed b Find the probability that none of the three have type B blood The probability that none of the three have type B blood is Round to three decimal places as needed c Find the probability that at least one of the three has type B blood The probability that at least one of the three has type B blood is Round to three decimal places as needed d Which of the events can be considered unusual Explain Select all that apply OA The event in part c is unusual because its probability is less than or equal to 0 05 OB None of these events are unusual OC The event in part b is unusual because its probability is less than or equal to 0 05 OD The event in part a is unusual because its probability is less than or equal to 0 05 7 of 40 people in the U CI

In a sample of 1200 U S adults 211 dine out at a resaurant more than once per week Two U S adults are selected at random from the population of all U S a without replacement Assuming the sample is representative of all U S adults complete parts a through d a Find the probability that both adults dine out more than once per week The probability that both adults dine out more than once per week is Round to three decimal places as needed b Find the probability that neither adult dines out more than once per week The probability that neither adult dines out more than once per week is Round to three decimal places as needed c Find the probability that at least one of the two adults dines out more than once per week The probability that at least one of the two adults dines out more than once per week is Round to three decimal places as needed d Which of the events can be considered unusual Explain Select all that apply A The event in part a is unusual because its probability is less than or equal to 0 05 B The event in part b is unusual because its probability is less than or equal to 0 05 C The event in part c is unusual because its probability is less than or equal to 0 05 D None of these events are unusual

Two cards are selected from a standard deck of 52 playing cards The first is replaced before the second card is selected Find the probability of selecting a heart and then selecting a nine The probability of selecting a heart and then selecting a nine is Round to three decimal places as needed 4

4 The table below shows the results of a survey in which 143 men and 145 women workers ages 25 to 64 were asked if they have at least one month s income set aside for emergencies Complete parts a through d Men Women Total 66 149 83 62 139 One month s income or more 77 Total 143 145 288 0 Less than one month s income a Find the probability that a randomly selected worker has one month s income or more set aside for emergencies The probability is Round to the nearest thousandth as needed b Given that a randomly selected worker is a male find the probability that the worker has less than one month s income The probability is Round to the nearest thousandth as needed c Given that a randomly selected worker has one month s income or more find the probability that the worker is a female The probability is Round to the nearest thousandth as needed d Are the events having less than one month s income saved and being male independent or dependent O Independent O Dependent

3 The table below shows the number of male and female students enrolled in nursing at a particular university for a recent semester a Find the probability that a randomly selected student is male given that the student is a nursing major b Find the probability that a randomly selected student is a nursing major given that the student is male Nursing Majors Non nursing majors Total 1148 2408 3556 C Males Females Total 92 733 825 1056 1675 2731 a Find the probability that a randomly selected student is male given that the student is a nursing major The probability is Round to three decimal places as needed b Find the probability that a randomly selected student is a nursing major given that the student is male The probability is Round to three decimal places as needed

17 A 100 kg uniform rectangular plate is supported in the position showr by hinges A and B and by cable DCE that passes over a frictionless hook at C Assuming that the tension is the same in both parts of the cable determine a the tension in the cable b the reactions at A and B Assume that the hinge at B does not exert any axial thrust Z y D 450 mm 90 mm 690 mm A C 960 mm 270 mm 90 mm B E 675 mm X

c Does 30 minutes of aerobic exercise each day provide significant improvement in mental performance To investigate this issue a researcher conducted a study with 150 adult subjects who performed aerobic exercise each day for a period of six months At the end of the study 200 variables related to the mental performance of the subjects were measured on each subject and the means compared to known means for these variables in the population of all adults Nine of these variables were significantly better in the sense of statistical significance at the a 0 05 level for the group that performed 30 minutes of aerobic exercise each day as compared to the population as a whole and one variable was significantly better at the a 0 01 level for the group that performed 30 minutes of aerobic exercise each day as compared to the population as a whole It would be correct to conclude O A that there is very good statistical evidence that 30 minutes of aerobic exercise each day provides improvement for the variable that was significant at the a 0 01 level We should be somewhat cautious about making claims for the variables that were significant at the a 0 05 level OB that there is very good statistical evidence that 30 minutes of aerobic exercise each day provides some improvement in mental performance C that these results would have provided very good statistical evidence that 30 minutes of aerobic exercise each day provides some improvement in mental performance if the number of subjects had been larger It is premature to draw statistical conclusions from studies in which the number of subjects is less than the number of variables measured OD none of the above

You and your friend are engaging in a classic sports argument which famous athlete is better at their respective sport In other words we re going to explore the question in the year 2022 was Jimmy Butler better at basketball than Tom Brady was at football Because we re comparing to totally different sports with different statistics in order to answer this question we need to look at standardized scores z scores For Tom Brady we ll look at passing yards Passing yards are a good way to measure a quarterback s ability to move the ball in short higher average passing yards per game is a good thing For Jimmy Butler we can look at points per game In the 2022 season Tom Brady had an average of 276 1 passing yards per game The total league average for the quarterbacks in the NFL was 226 19 with a standard deviation of 37 80 Using this information tell me who was better Tom Brady or Jimmy Butler and why In your answer include the following information a The z scores for Tom Brady s passing yards and Jimmy Butler s points per game Hint you already calculated the z score for Jimmy Butler in the questions above b A comparison of the two z scores an explanation of your conclusion based on those z scores What is your final conclusion who is better relative to others in their respective sports Why