Statistics Questions

4 6 Poisson 117 The switchboard in a Minneapolis law office gets an average of 5 5 incoming phone calls during the noon hour on Mondays Experience shows that the existing staff can handle up to six calls in an hour Let X the number of calls received at noon a Find the mean and standard deviation of X b What is the probability that the office receives at most six calls at noon on Monday c Find the probability that the law office receives six calls at noon What does this mean to the law office staff who get on average 5 5 incoming phone calls at noon d What is the probability that the office receives more than eight calls at noon with an average of 60

104 A consumer looking to buy a used red sports car will call dealerships until she finds a dealership that carries the car She estimates the probability that any independent dealership will have the car will be 28 percent We are interested in the number of dealerships she must call a In words define the random variable X b List the values that X may take on c Give the distribution of X X d On average how many dealerships would we expect her to have to call until she finds one that has t car

f Find the probability that at most three on the committee are not 115 Suppose that nine Massachusetts athletes are scheduled to appear at a charity benefit The nine are randomly chosen from eight volunteers from the local basketball team and four volunteers from the local football team We are interested in the number of football players picked a In words define the random variable X b List the values that X may take on c Give the distribution of X X d Are you choosing the nine athletes with or without replacement lected at random and without replacement from a deck of 52

able 93 A student takes a 32 question multiple choice exam but did not study and randomly guesses each answer Each question has three possible choices for the answer Find the probability that the student guesses more than 75 percent of the questions correctly

1 000 babies in an intensive care nursery Suppose that 1 000 babies from healthy baby nurseries were randomly surveyed Find the probability that exactly two babies were born deaf Use the following information to answer the next four exercises Recently a nurse commented that when a patient calls the medical advice line claiming to have the flu the chance that he or she truly has the flu and not just a nasty cold is only about 4 percent Of the next 25 patients calling in claiming to have the flu we are interested in how many actually have the flu 83 Define the random variable and list its possible values 84 State the distribution of X 85 Find the probability that at least four of the 25 patients actually have the flu 36 On average for every 25 patients calling in how many do you expect to have the flu 87 People visiting video rental stores often rent more than one DVD at a time The probability distribution for DVD rentals per customer at Video to Go is given Table 4 37 There is a five video limit per customer at this store so nobody ever rents more than five DVDs X 0 1 2 3 4 5 Table 4 37 P x 03 50 24 07 04 a Describe the random variable X in words b Find the probability that a customer rents three DVDs

ble Use the following information to answer the next two exercises The average number of times per week that Mrs Plum s cats wake her up at night because they want to play is 10 We are interested in the number of times her cats wake her up each week 128 In words what is the random variable X a the number of times Mrs Plum s cats wake her up each week b the number of times Mrs Plum s cats wake her up each hour c the number of times Mrs Plum s cats wake her up each night d the number of times Mrs Plum s cats wake her up 2 129 Find the probability that her cats will wake her up no more than five times next week a 5000 b 9329 c 0378 d 0671

118 The maternity ward at a hospital in the Philippines is one of the busiest in the world with an average of 60 births per day Let X the number of births in an hour a Find the mean and standard deviation of X b Sketch a graph of the probability distribution of X c What is the probability that the maternity ward will deliver three babies in one hour d What is the probability that the maternity ward will deliver at most three babies in one hour e What is the probability that the maternity ward will deliver more than five babies in one hour up that 3 percent of its bulbs are defective Using both the

109 Ellen has music practice three days a week She practices for all of the three days 85 percent of the time two days 8 percent of the time one day 4 percent of the time and no days 3 percent of the time One week is selected at random What values does X take on

111 According to a recent poll 75 percent of millennials people born between 1981 and 1995 have a profile on a social networking site Let X the number of millennials you ask until you find a person without a profile on a social networking site a Describe the distribution of X b Find the 1 mean and ii standard deviation of X c What is the probability that you must ask 10 people to find one person without a social networking site d What is the probability that you must ask 20 people to find one person without a social networking site phobility that you must ask at most five people

orten rent more than one DVD at a time The probability distribution for DVD rentals per customer at Video to Go is given in the following table There is a five video limit per customer at this store so nobody ever rents more than five DVDs 0 1 2 3 4 5 Table 4 35 X 0 1 2 a Describe the random variable X in words b Find the probability that a customer rents three DVDs c Find the probability that a customer rents at least four DVDs 3 d Find the probability that a customer rents at most two DVDs Another shop Entertainment Headquarters rents DVDs and video games The probability distribution for DVD rentals per customer at this shop is given as follows They also have a five DVD limit per customer 4 P x 5 03 Table 4 36 50 24 70 04 P x 35 25 20 10 05 05 V e At which store is the expected number of DVDs rented per customer higher f If Video to Go estimates that they will have 300 customers next week how many DVDs do they expect to rent next week Answer in sentence form g If Video to Go expects 300 customers next week and Entertainment Headquarters projects that they will have 420 customers for which store is the expected number of DVD rentals for next week higher Explain h Which of the two video stores experiences more variation in the number of DVD rentals per customer How do you know that

Use the following information to answer the next three exercises The probability that a local hockey team will win any given game is 0 3694 based on a 13 year win history of 382 wins out of 1 034 games played as of a certain date An upcoming monthly schedule contains 12 games 89 What is the expected number of wins for that upcoming month a 1 67 b 12 382 C 1043 d 4 43

100 It has been estimated that only about 30 percent of California residents have adequate earthquake supplies Suppose you randomly survey 11 California residents We are interested in the number who have adequate earthquake supplies a In words define the random variable X b List the values that X may take on c Give the distribution of X X d What is the probability that at least eight have adequate earthquake supplies e is it more likely that none or that all of the residents surveyed will have adequate earthquake supplies Why f How many residents do you expect will have adequate earthquake supplies

79 A friend offers you the following deal For a 10 fee you may pick an envelope from a box containing 100 seemingly identical envelopes However each envelope contains a coupon for a free gift Ten of the coupons are for a free gift worth 6 Eighty of the coupons are for a free gift worth 8 Six of the coupons are for a free gift worth 12 Four of the coupons are for a free gift worth 40 Based upon the financial gain or loss over the long run should you play the game a Yes I expect to come out ahead in money b No I expect to come out behind in money c It doesn t matter I expect to break even cileble

76 Suppose that 20 000 married adults in the United States were randomly surveyed as to the number of children they have The results are compiled and are used as theoretical probabilities Let X the number of children married people have X 0 1 2 3 4 5 6 or more Table 4 33 P x 10 20 30 10 05 05 xP x a Find the probability that a married adult has three children b In words what does the expected value in this example represent c Find the expected value d Is it more likely that a married adult will have two to three children or four to six children How do you know porn a bachelor of science B S degree is given

1 Name 2 Liam Henry 3 4 Ellie 5 Chloe 6 Daniel 7 Luke 8 Sophie 9 Joseph 10 Lewis 11 William 12 Charlotte 13 Holly 14 Adam 15 Amy 16 Emily 17 James 18 Joshua 19 Callum 20 Megan 21 Matthew 22 Katie 23 Samuel 24 Rebecca 25 Benjamin 26 Bethany 27 Jessica 28 Olivia 29 Thomas 30 Jack 31 32 Highest score Person name 33 Highest score 34 Mean score 35 Median score 36 Standard deviation 37 33 A 38 B Grade NRRONDOXXONRKNORONOS 72 73 73 65 77 68 69 85 83 68 66 66 93 71 87 70 68 84 75 78 68 71 63 65 70 66 77 68 65 93 72 551724 70 C

a About what percent of the cheese last between 10 and 15 days P 10 x 15 21 10 15 5 1 6 3 P 10 x415 0 0548 0 9452 F 94 527 b About what percent of the cheese last between 13 and 16 days D 13 x 14 2 1 13 10 13 16 3 3 c The oldest 10 of cheese are put on sale These cheeses will be older than what age d From a random selection of 60 cheeses how many would you expect to be over a week old

Textbook prices have a seasonal structure on Ebay At the end of a term the supply of used books outstrips demand and the price is lower Near the start of a term many students are looking for books and the price is higher Suppose we can classify sales for a particular chemistry textbook into these two time periods and an other time period in the proportions shown below We have also listed the average price the textbook sells for in each of these three time periods Sales proportion Average price Start of term 0 45 82 52 End of term 0 31 49 12 Other 0 24 65 23 For example about 45 of Ebay auctions for this chemistry textbook occur at the start of the term and the books sell for an average of 82 52 during this time Using the information above compute the average price of the textbook over all seasons Do not put a dollar sign in your answer

The Blacktop Speedway is a supplier of automotive parts Included in stock are 12 speedometers that are correctly calibrated and two that are not Three speedometers are randomly selected without replaceme Let the random variable a represent the number that are not correctly calibrated Complete the probability distribution table Report probabilities accurate to 4 decimal places P x X 0 1

Keke s Kookies https kekekookies com sells mini cookies in packs of 5 and has determined a probability distribution for the number of cookies that they sell in a given day down X sold 0 5 10 15 20 Probability 0 21 0 12 0 37 0 11 a What is the probability of selling 15 mini cookies in a given day b Find the expected number of mini cookies sold in a day using the discrete probability distribution

2 0 1 2 3 P x 0 2 0 05 0 3 0 45 a Find the expected value of the probability distribution Round to two decimal places b Find the standard deviation of the probability distribution Round to two decimal place

Find the mean of the following probability distribution Round your answer to one decimal X P x 0 0 0947 1 0 0965 2 0 1102 3 0 4188 4 0 2799

The following table represents the probability of the number of cars owned by a college student Give your answer to at least 3 decimal places X 0 1 2 3 P x 0 5 0 35 0 12 0 03 a Is this a valid discrete probability distribution Select an answer b Find the mean number of cars owned c Find the standard deviation of the number of ca d Find 2 Question Help Message instructor Submit Question Select an answer No since P x 1 and 0 P x 1 Yes since P x 1 and 0 P x 1 Yes since P x 1 and P x 0

K The accompanying data represent the monthly rate of return of a certain company s common stock for the past few years Complete parts a and b below Click the icon to view the data table a Determine and interpret the quartiles The first quartile is Q Round to four decimal places as needed The second quartile is Q Round to four decimal places as needed The third quartile is Q3 Round to four decimal places as needed Interpret the quartiles Choose the correct answer below OA The first quartile is the lower bound of plausible monthly returns and the third quartile is the upper bound of plausible monthly returns Any monthly returns outside of these bounds are outliers The second quartile represents the most common monthly return OB The first quartile is one standard deviation below the mean or average monthly return the second quartile is the mean and the third quartile is one standard deviation above the mean OC Of the monthly returns 25 are less than or equal to the first quartile 50 are less than or equal to the second quartile and 75 are less than or equal to the third quartile O D All monthly returns within one standard deviation of the mean are contained in the first quartile all monthly returns within two standard deviations of the mean are contained in the second quartile and all monthly returns within three standard deviations of the mean are contained in the third quartile b Check the data set for outliers Select the correct choice below and if necessary fill in the answer box to complete your choice OA The outlier s is are Type an integer or a decimal Do not round Use a comma to separate answers as needed B There are no outliers in the data set

In Marissa s calculus course attendance counts for 20 of the grade quizzes count for 15 of the grade exams count for 45 of the grade and the final exam counts for 20 of the grade Marissa had a 100 average for attendance 93 for quizzes 82 for exams and 81 on the final Determine Marissa s course average Marissa s course average is Type an integer or a decimal Do not round

Caleb Martin Cody Zeller Dewayne Dedmon Dru Smith Duncan Robinson Gabe Vincent Haywood Highsmith Jamal Cain Jamaree Bouyea Jimmy Butler Kevin Love Kyle Lowry Max Strus Nikola Jovic Omer Yurtseven Orlando Robinson Tyler Herro Udonis Haslem 9 6 6 5 5 7 2 2 6 4 9 4 4 4 5 4 3 8 22 9 7 7 11 2 11 5 5 5 4 4 3 7 20 1 3 9

You purchase a car for 30 000 using a five year car loan The loan has an APR of 6 What is your monthly car payment Construct an amortization table for the loan Must be done in Excel

The probability that a randomly selected 4 year old male garter snake will live to be 5 years old is 0 95842 a What is the probability that two randomly selected 4 year old male garter snakes will live to be 5 years old b What is the probability that five randomly selected 4 year old male garter snakes will live to be 5 years old c What is the probability that at least one of five randomly selected 4 year old male garter snakes will not live to be 5 years old Would it be unusual if at least one of five randomly selected 4 year old male garter snakes did not live to be 5 years old a The probability that two randomly selected 4 year old male garter snakes will live to be 5 years old is Round to five decimal places as needed b The probability that five randomly selected 4 year old male garter snakes will live to be 5 years old is Round to five decimal places as needed c The probability that at least one of five randomly selected 4 year old male garter snakes will not live to be 5 years old is Round to five decimal places as needed 0 05 Would it be unusual if at least one of five randomly selected 4 year old male garter snakes did not live to be 5 years old because the probability of this happening is

Suppose that events E and F are independent P E 0 6 and P F 0 9 What is the P E and F The probability P E and F is intener or a decimal

Suppose you just purchased a digital music player and have put 11 tracks on it After listening to them you decide that you like 2 of the songs With the random feature on your player each of the 11 songs is played once in random order Find the probability that among the first two songs played a You like both of them Would this be unusual b You like neither of them c You like exactly one of them d Redo a c if a song can be replayed before all 11 songs are played

Suppose the data below represent in thousands the type of health insurance coverage of people by age Determine P 18 years old and P 18 years old no health insurance Are the events 18 years old and no health insurance independent Age Private health insurance Government health insurance No health insurance Total 18 18 44 44 055 73 781 20 801 11 297 8 663 28 422 73 519 45 64 58 297 10 625 10 803 113 500 79 725 P 18 years old Round to three decimal places as needed 64 25 989 39 822 899 66 710 S Total 202 122 82 545 48 787 333 454

Suppose you just received a shipment of eight televisions Four of the televisions are defective If two televisions are andomly selected compute the probability that both televisions work What is the probability at least one of the two televisions does not work The probability that both televisions work is logos as needed

Due to a manufacturing error six cans of regular soda were accidentally filled with diet soda and placed into a 18 pack Suppose that two cans are randomly selected from the 18 pack Complete parts a through c a Determine the probability that both contain diet soda Round to four decimal places as needed with

Suppose that E and F are two events and that P E 0 6 and P FIE 0 2 What is P E and F P E and F

A family has six children If this family has exactly three boys how many different birth and gender order are possible There are different birth and gender orders possible Type a whole number

A player is dealt 5 cards from a standard 52 card deck Determine the probability of being dealt two of a kind such as two aces or two kings by answering questions a through d a How many ways can 5 cards be selected from a 52 card deck ways that 5cards can be selected from a 52 card deck hor There are

6 1 Refer to the oil spill case study a What are the populations of interest b What are some factors other than flora density that may indicate that the oil sp has affected the marsh c Describe a method for randomly selecting the tracts where flora density measu ments were to be taken d State several hypotheses that may be of interest to the researchers

O 9 In its monthly report the local animal shelter states that it currently has 24 dogs and 18 cats available for adoption Eight of the dogs and 6 of the cats are male Find each of the following conditional probabilities if an animal is selected at random Hint create a two way table a Pipet is male cat b P pet is cat female c P pet is female dog 10 A private college report contains these statistics 70 of incoming freshmen attended public schools 75 of public school students who enroll as freshmen eventually graduate 90 of other freshmen eventually graduate Based on the probabilities given what percent of freshmen eventually graduate Hint organize the information in a tree diagram Answers 3 a 52 b S 888 BBG BGB BGG GBB GBG GGB GGG 1 7 6 a 8 b 8 6 9 2 a 36 b 36 b 52 12 a 2652 a 10 000 al combination 676 b 2652 c 8 c 36 16 c 52 24 c 132600 b 1 757 600 8 d 36 d c 2 433 600 6 20 20 e 36 e 52 d 916 132 832 c permutation d combination 7 a 20 1 720 8 a 0 06 b 10 120 d 120 g 120 b 0 50 0 94 0 429 0 333 9 a 18 10 79 5 12 b 28 16 c 24 e 13 983 87 0 667

Suppose that you are buying a car for 60 000 You saved 20 000 for a down payment The dealer is offering you two incentives Incentive A is a 5000 off the price of the car followed by a five year loan at 7 39 compounded monthly Incentive B does not have a cash rebate but provides free financing no interest over five years What is the difference between the monthly payments for the two offers Which incentive is the better deal P Payment nxt approximately 33 Incentive B is the better deal approximately 15 Incentive A is the better deal approximately 85 Incentive B is the better deal approximately 67 Incentive A is the better deal

A poll reported that 64 of adults were satisfied with the job the major airlines were doing Suppose 15 adults are selected at random and the number who are satisfied is recorded Complete parts a through e below a Explain why this is a binomial experiment Choose the correct answer below OA This is a binomial experiment because there are two mutually exclusive outcomes for each trial there is a fixed number of trials the outcome of one trial does not affect the outcome of another and the probability of success is the same for each trial B This is a binomial experiment because there are two mutually exclusive outcomes for each trial there is a fixed number of trials the outcome of one trial does not affect the outcome of another and the probability of success changes in each trial OC This is a binomial experiment because there are two mutually exclusive outcomes for each trial there is a random number of trials the outcome of one trial does not affect the outcome of another and the probability of success is the same for each trial OD This is a binomial experiment because there are three mutually exclusive outcomes for each trial there is a fixed number of trials the outcome of one trial does not affect the outcome of another and the probability of success is the same for each trial

Calculate the future value Round your answer to two decimal places P 27 000 r 7 compounded monthly t 4 years

Find the value of the combination 12 C6

Find the value of the factorial 7

14 Use the following information to calculate MSE Round your answer to the nearest thousandths x 5 5 X 4 4 X3 6 2 n 14 n 14 n3 16 s 4 2 s 3 8 s 3 5 4 Round your answer to the nearest thousandths Answer Previous Answer 12 190

7 What is the slope of the least squares regression line for the data 1 2 3 4 5 6 7 8 8 6 Round your answer to the nearest hundredths Answer Previous Answer 0 71

Question 5 of 14 5 What is the second coordinate of the point at which the line y 0 5x 1 5 crosses the y axis Answer Previous Answer 1 5

8 How many units does the point 2 4 vertically deviate above the line y 2x 2 r MyHer Previous Answer Return to overview

Question 4 of 14 4 What is the slope of the line passing through the points 1 2 and 4 6 Answer Previous Answer 0 8

6 19 Student study times A class survey in a large class for first year college students asked About how many hours do you study during a typical week The mean response of the 463 students was as x 13 7 hours 6 Sup pose that we know that the study time follows a Normal distribution with standard deviation o 7 4 hours in mobo the population of all first year students at this university boird a Use the survey result to give a 99 confidence inter val for the mean study time of all first year students b What condition not yet mentioned must be met for onfidence interval to be valid

9 Sample Size and Margin of Error Example 16 1 page 377 described NHANES survey data on the body mass index BMI of 654 young women The mean BMI in the sample was x 26 8 We treated these data as an SRS from a Normally distributed population with standard deviation o 7 5 1 a Suppose that we had an SRS of just 100 young women What would be the margin of error for 95 confidence b Find the margins of error for 95 confidence based on SRSS of 400 young women and 1600 young women c Compare the three margins of error How does increasing the sample size change the margin of error of a confidence interval when the confidence level and population standard deviation remain the same

lo plain the confidence interval for mean ideal weight de scribed in the previous exercise The student answers We can be 95 confident that future samples of adult American women will say that their mean ideal weight is between 137 7 and 140 3 pounds Is this explanation cor rect Explain your answer Hint See the box Interpreting a Confidence Level on page 379