Statistics Questions

Assume that a sample is used to estimate a population proportion p Find the margin of error M E that corresponds to a sample of size 226 with 45 1 successes at a confidence level of 95 M E Answer should be obtained without any preliminary rounding However the critical value may be rounded to 3 decimal places Round final answer to one decimal place

The random variables X and Y have the following joint density function 3 f x y xy 3 x 0 x 2 0 y 1 and equal to 0 otherwise a Are X and Y independent b Find E X c Find E Y d Find Var X e Find Var Y a Select the correct choice and fill in the answer box to complete your choice O A X and Y are independent because f x y is not equal to fx x fy y O B X and Y are not independent because f x y is equal to fx x fy y OC X and Y are independent because f x y is equal to fx x fy y denendent honoun fleul in not oualtof huulf ful

Let f x y 2xy where 0 x 2 0 sy 2 0 x y 2 and let it equal 0 otherwise a Show that f x y is a joint probability density function b Find E X c Find E Y a Find an expression that when solved will show that the function is a joint density function Select the correc answer and fill in the answer box to complete your choice Simplify your answer 2 X IT OA OC 1 5 00 3 2xy dxdy www 3 Zxy dydx OB OD 0 X 3 zxy 11 3 0 X dxdy 2xy dydx

Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car They randomly survey 410 drivers and find that 309 claim to always buckle up Construct a 95 confidence interval for the population proportion that claim to always buckle up Use Brackets for interval

You measure 48 dogs weights and find they have a mean weight of 42 ounces Assume the population standard deviation is 2 8 ounces Based on this construct a 90 confidence interval for the true population mean dog weight Note you will use the z distribution for your critical valu since the population standard deviation is given Write your answer in the form of point estimate margin of error Give your answers as decimals to two places ounces Write your answer using inequality notation

Express the confidence interval 88 6 8 3 in interval form

We wish to estimate what percent of adult residents in a certain county are parents Out of 100 adult residents sampled 11 had kids Based on this construct a 99 confidence interval for the proportion p of adult residents who are parents in this county Give your answers as decimals to three places

The accompanying table gives the joint probability mass function for X and Y a Find E X and E Y b Find Var X and Var Y c Find Cov X Y d Find the correlation between X and Y Click the icon to view the joint probability mass function for X and Y Joint Probability Mass Function X p x y 123 0 13 0 06 0 07 y 0 09 0 12 0 07 3 0 15 0 11 0 20 u X

If X X2 X3 and X4 are pairwise uncorrelated random variables each having mean 1 and variance 1 comp the correlations of a X X and X X3 b X X and X3 X4 1 a p X X X X3 2 Type an exact answer in simplified form b p X X X3 X4 4 Type an exact answer in simplified form HI

There are 4 different types of coupons the first 2 of which comprise one group and the second 2 another group Eac 1 H Find the expected number of 10 new coupon obtained is type i with probability P where P P2 P3 P4 coupons that one must obtain to have at least one of a all 4 types b all the types of the first group c all the types of the second group d all the types of either group a The expected number of coupons is Type an integer or a simplified fraction 2

The number of accidents that a person has in a given year is a Poisson random variable with mean However suppose that the value of changes from person to person being equal to 2 for 60 percent of the population and 4 for the other 40 percent If a person is chosen at random what is the probability that he will have a 0 accidents and b exactly 3 accidents in a certain year What is the conditional probability that he will have 3 accidents in a given year given that he had no accidents the preceding year a The probability that he will have 0 accidents is Type an integer or decimal rounded to three decimal places as needed

For a group of 140 people compute a the expected number of days of the year that are birthdays of exactly 2 people b the expected number of distinct birthdays EEI a The expected number of days of the year that are birthdays of exactly 2 people is Round to four decimal places as needed

A prisoner is trapped in a cell containing 3 doors The first door leads to a tunnel that returns him to his cell after 2 days travel The second leads to a tunnel that returns him to his cell after 5 days travel The third door leads to freedom after 1 day of travel If it is assumed that the prisoner will always select doors 1 2 and 3 with respective probabilities 0 4 0 5 and 0 1 what is the expected number of days until the prisoner reaches freedom The expected number of days until the prisoner reaches freedom is Type an integer or a decimal Do not round C U L ZZZZZ 2 CE S 160

here are two misshapen coins in a box their probabilities for landing on heads when they are flipped are espectively 0 4 and 0 7 One of the coins is to be randomly chosen and flipped 9 times Given that two of the first hree flips landed on heads what is the conditional expected number of heads in the 9 flips The conditional expected number of heads in the 9 flips is Round to three decimal places as needed

If X X X3 and X4 are pairwise uncorrelated random variables each having mean 1 and variance 1 compute the correlations of a X X and X X3 b X X and X3 X4 a p X X X X3 Type an exact answer in simplified form

A miner is trapped in a mine containing 3 doors The first door leads to a tunnel that will take him to safety after 4 hours of travel The second door leads to a tunnel that will return him to the mine after 6 hours of travel The third door leads to a tunnel that will return him to the mine after 5 hours If it is assumed that the miner is at all times equally likely to choose any one of the doors what is the variance of the length of time until the miner reaches safety The variance of the length of time until the miner reaches safety is Type an integer or a simplified fraction

A pond contains 100 fish of which 27 are carp If 15 fish are caught what are the mean and variance of the number of carp among the 15 What assumptions are you making Let X denote the number of carp caught of the 15 fish caught What assumptions are you making Type your answers as integers or decimals Do not round O A X satisfies a hypergeometric distribution with parameters n N and o O B X satisfies a normal distribution with parameters OC X satisfies a exponential distribution with parameter OD X satisfies a binomial distribution with parameters n 6980336 and p and m

Suppose that the expected number of accidents per week at an industrial plant is 4 Suppose also that the numbers of workers injured in each accident are independent random variables with a common mean of 2 6 If the number of workers injured in each accident is independent of the number of accidents that occur compute the expected number of workers injured in a week The expected number of workers injured in a week is Type an integer or a decimal Do not round

If E X 1 and Var X 3 find a E 4 x b Var 2 4X a E 4 x Type an integer or a simplified fraction

Cards from an ordinary deck are turned face up one at a time Compute the expected number of cards that need to be turned face up in order to obtain a 2 aces b 6 spades c all 13 diamonds HE a The expected number of cards that need to be turned face up in order to obtain 2 aces is Round to one decimal place as needed ct 0

A fair die is rolled 20 times Calculate the variance of the sum of the rolls The expected sum of the 20 rolls is Type an integer or a simplified fraction HI

A player throws a fair die and simultaneously flips a fair coin If the coin lands heads then she wins one third and if tails then she wins one half of the value that appears on the die Determine her expected winnings The expected winnings are Type an integer or a simplified fraction

3 43789 145 9463 Lap to thousandths Lap to tenths

If n 11 a 37 and s 4 construct a confidence interval at a 80 confidence level Assume the dat came from a normally distributed population Give your answers to one decimal place

If n 20 30 and s 2 construct a confidence interval at a 99 confidence level Give you answers to one decimal place

Researchers observed 50 random people brush their teeth and recorded the number of seconds each person spent brushing From the sample they found a mean time of 41 7 seconds Further their calculations revealed that this estimate is within a margin of error of 2 15 from the true average time that all people spend brushing their teeth Write the interval estimate that will estimate the true average time that people spend brushing their teeth Write your answer in interval notation Write your answer using inequality notation ft

Express the confidence interval 61 3 5 3 in interval form Express the answer in decimal format do not enter as perceptr

In a random sample of 185 elementary school students 39 could speak at least two languages This resulted in a 95 confidence interval of 0 32 0 46 If nothing else changes how will the following intervals compare a A 90 confidence interval wider narrower b A 99 confidence interval wider narrower c A confidence interval where 48 spoke at least two languages wider narrower d A confidence interval where 19 spoke at least two languages wider narrower e A confidence interval using n 235 wider narrower f A confidence interval using n 110

A confidence interval for the population mean number of jobs a person has before the age of forty was found to be 8 1 to 10 4 Find the midpoint of this confidence interval

A student was asked to find a 99 confidence interval for widget width in mm using data from a random sample of size n 20 Which of the following is a correct interpretation of the interval 13 6 32 6 Check all that are correct With 99 confidence the mean width of all widgets is between 13 6 mm and 32 6 mm With 99 confidence the mean width of a randomly selected widget will be between 13 6 mm and 32 6 mm There is a 99 chance that the mean of a sample of 20 widgets will be between 13 6 mm and 32 6 mm There is a 99 chance that the mean of the population is between 13 6 mm and 32 6 mm The mean width of all widgets is between 13 6 mm and 32 6 mm 99 of the time We know this is true because the mean of our sample is between 13 6 mm and 32 6 mm

In a survey 22 people were asked how much they spent on their child s last birthday gift The results were roughly bell shaped with a mean of 38 and standard deviation of 4 Construct a confidence interval at a 90 confidence level Give your answers to one decimal place

The city wishes to estimate the average commute distance for all city employees They collect a random sample of 64 employees and find a sample mean of 7 3 miles They also assume a population standard deviation of a 1 8 miles Calculate the z interval to estimate the average o commute distance for all city employees with 95 confidence Round your answers to 2 decimal places Find the Critical Value z Point Estimate Margin of Error Write the interval as lower bound upper bound

The reading speed of second grade students in a large city is approximately normal with a mean of 90 words per minute wpm and a standard deviation of 10 wpm Complete parts a through f c What is the probability that a random sample of 20 second grade students from the city results in a mean reading rate of more than 96 words per minute The probability is Round to four decimal places as needed Interpret this probability Select the correct choice below and fill in the answer box within your choice OA If 100 independent samples of n 20 students were chosen from this population we would expect sample s to have a sample mean reading rate of exactly 96 words per minute OB If 100 independent samples of n 20 students were chosen from this population we would expect sample s to have a sample mean reading rate of more than 96 words per minute OC If 100 independent samples of n 20 students were chosen from this population we would expect sample s to have a sample mean reading rate of less than 96 words per minute d What effect does increasing the sample size have on the probability Provide an explanation for this result OA Increasing the sample size increases the probability because o decreases as n increases increases as n increases OB Increasing the sample size increases the probability because o OC Increasing the sample size decreases the probability because o decreases as n increases O D Increasing the sample size decreases the probability because o increases as n increases e A teacher instituted a new reading program at school After 10 weeks in the program it was found that the mean reading speed of a random sample of 18 second grade students was 92 1 wpm What might you conclude based on this result Select the correct choice below and fill in the answer boxes within your choice Type integers or decimals rounded to four decimal places as needed OA A mean reading rate of 92 1 wpm is unusual since the probability of obtaining a result of 92 1 wpm or more is This means that we would expect a mean reading rate of 92 1 or higher from a population whose mean reading is 90 in of every 100 random samples of size n 18 students The new program is abundantly more effective than the old program OB A mean reading rate of 92 1 wpm is not unusual since the probability of obtaining a result of 92 1 wpm or more is This means that we would expect a mean reading rate of 92 1 or higher from a population whose mean reading rate is 90 in of every 100 random samples of size n 18 students The new program is not abundantly more effective than the old program f There is a 5 chance that the mean reading speed of a random sample of 24 second grade students will exceed what value There is a 5 chance that the mean reading speed of a random sample of 24 second grade students will exceed wpm Round to two decimal places as needed

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 0 Round to four decimal places as needed The first quartile is Q The second quartile is Q2 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 Rate of Return 0 26 0 03 0 06 0 19 0 26 0 48 0 06 0 16 0 08 0 05 0 02 0 02 0 06 0 01 0 07 0 05 0 01 0 06 0 04 0 04 0 22 0 05 0 18 0 09 0 02 0 02 0 13 0 08 0 02 0 01 0 10 0 02 0 10 0 25 0 02 0 09 0 11 0 11 0 03 0 03 0 X artile is the upper bound of ers The second quartile return the second quartile ess than or equal to the he first quartile all monthly quartile and all monthly uartile in the answer box to comple

A sample was done collecting the data below Calculate the standard deviation to one decimal place X 30 23 5 20

If a person invests 2 000 at 3 interest compounded monthly how long will it take for the investment to grow to 3 000 Use the formula 4 1 P 1 2 5 pts

A sample was done collecting the data below Calculate the standard deviation to one decimal place X 21 9

A student took five exams in a course last semester The scores are shown below 84 95 94 96 90 Calculate the mean variance and standard deviation Round to 4 decimal places when needed and use rounded answers for future calculations The mean is The variance is o The standard deviation in

A teacher surveys 39 of the current 344 enrolled students at a local college What is the size of the sample What is the size of the population

Find the width between the interval 6 7

There are 84 shoppers in the market a salesperson surveys 35 peop What is the size of the population What is the size of the sample

The useful life of a bicycle bought at Basement mart fits a log normal distribution with a mean of 15 months and a standard deviation of 13 92 months Suppose that 68 bicycles are randomly chosen and let X the average useful life of a bicycle bought at Basement mart from a sample of 68 bicycles in months X

A particular fruit s weights are normally distributed with a mean of 321 grams and a standard deviation of 26 grams If you pick 20 fruits at random then 10 of the time their mean weight will be greater than how many grams Give your answer to the nearest gram

Suppose that the value of stock varies each day from 14 to 25 with a uniform distribution Find the 20th percentile O2 2 O 14 2 O 22 8

Which of the following is NOT a characteristic of the chi square distribution The mean of the chi square distribution is located to the left of the peak The chi square curve is nonsymmetrical The chi square curve approaches but never touches the positive horizontal axis As the degrees of freedom increases the chi square curves look more and more like a normal curve

In a survey of 356 people who attended a local professional soccer team s most recent home game 135 said that they were fans of the visiting team Create a 95 confidence interval for the population proportion of attendees who were fans of the visiting team Use a TI 84 plus calculator rounding your answers to three decimal places

The following data was calculated during a study on weight loss Interpret the p value for this hypothesis test A doctor would like to test the claim that the average weight loss after participating in a diet program is less than 10 pounds The test statistic is calculated as Zo 2 5 The p value is 0 0062 The probability of the observing value Zo 2 5 or greater if the null hypothesis is true is 99 38 The probability of the observing value Zo 2 5 or less if the null hypothesis is true is 99 38 O The probability of the observing value Zo 2 5 or greater if the null hypothesis is true is 0 62 O The probability of the observing value Zo 2 5 or less if the null hypothesis is true is 0 62

A health and fitness club reviews the weights of all of their members and found that the average weight was 148 lb Is this value a statistic or a parameter O Statistic O Parameter

A test consists of 10 multiple choice questions each with five possible answers one of which is correct To pass the test a student must get 60 or better on the test If a student randomly guesses what is the probability that the student will pass the test 0 0 006 O 0 205 0060

A manager wishes to determine the relationship between the number of miles in hundreds of miles the manager s sales representatives travel per month and the amount of sales in thousands of dollars per month Find the test statistic Miles traveled x Sales y O 1 89 632 22 062 2 23 31 3 c 22 000 15 3 1 120