Statistics Questions

Question 9 of 15 Suppose X is a binomial random variable with 10 trials and success probability 0 60 Find the mean of X Answer Previous Answer 6

An experiment is to draw 1 card from a fair deck of playing cards a If you were to list the sample space how many equally likely outcomes would it have b Find the probability of getting a 7 Leave your answer as a fraction c Find the probability of not getting a diamond Leave your answer as a fraction d Find the probability of getting a spade Leave your answer as a fraction e Find the probability of getting a 7 or a club Leave your answer as a fraction

You roll two fair dice a If you were to list the sample space for this problem how many equally likely outcomes would there be b Find the probability of getting a sum of 9 Leave your answer as a fraction c Find the probability of getting a 5 on the first die Leave your answer as a fraction d Find the probability of getting a sum of 9 AND a 5 on the first die Leave your answer as a fraction e Find the probability of getting a sum of 9 OR a 5 on the first die Leave your answer as a fraction f Find the probability of getting doubles Leave your answer as a fraction g Find the probability of getting both dice to be odd numbers Leave your answer as a fraction h Find the probability of getting doubles AND both dice to be odd numbers Leave your answer as a fraction i Find the probability of getting doubles OR both dice to be odd numbers

Eyeglassomatic manufactures eyeglasses for different retailers They test to see how many defective lenses they made in a time period The folllowing table gives the type of defect and the number of lenses with that defect Assume categories are mutually exclusive Defect Type Scratch Right shaped small Flaked Wrong axis Chamfer wrong Crazing cracks Wrong shape Wrong PD Spots and bubbles Wrong height Right shape big Lost in lab intern Spots bubbles Frequency 5621 4672 1803 1418 1775 1561 1583 1550 1410 1123 1348 991 990 a Find the probability that a randomly selected defect from the table will be in the categor Right shaped small or the category Wrong axis Give your answer as a fraction Give your answer rounded to three decimal places b Find the probability that a randomly selected defect is not in the category Right shaped small Given your answer as a fraction Give your answer rounded to three decimal places

A fair coin is flipped three times a State the sample space List outcomes separated by commas Use notation like HTT to mean the first toss was heads the second toss was tails and the third toss was tails b Find the probability of getting exactly two heads Leave your answer as a fraction c Find the probability of getting at least 1 tail Leave your answer as a fraction d Find the probability of getting an odd number of tails Leave your answer as a fraction e Find the probability of getting all heads or all tails Leave your answer as a fraction f Find the probability of getting exactly two heads or exactly two tails Leave your answer as a fraction g Find the probability of not getting at least 1 tail Leave your answer as a fraction

In the game of roulette there is a wheel with spaces marked 0 through 36 and a space marked 00 a Find the probability of winning if you pick the number 26 and it comes up on the wheel Leave your answer as a fraction b Find the probability of an odd number coming up on the wheel Leave your answer as a fraction

The number of M Ms of each color that were found in a case with M Ms is given in the table below color Freq blue 286 brown green orange red yellow 243 220 219 117 346 a Find the probability that a randomly selected M M will be in the category blue or brown Give your answer as a fraction Give your answer rounded to three decimal places Give your answer rounded to three decimal places b Find the probability that a randomly selected M M is not in the category blue Given your answer as a fraction

An experiment is pulling a ball from an urn that contains 8 blue balls and 8 red balls a Find the probability of getting a blue ball Leave your answer as a fraction b Find the probability of getting a red ball Leave your answer as a fraction

Rewrite this number in appropriate scientific notation 1 320 000 answer

Rewrite this number in appropriate scientific notation 0 000141

Write the number in scientific notation 0 081 Question Help Moccago in

Write the number in scientific notation 74 000

The world population is estimated to be about 7 600 000 000 people Which answer expresses this number in scientific notation 0 076 x 10 0 07 x 10 076 x 108 07 6 x 109

Which means the same as 5 1411 x 105 514110 O 5141 1 5141100 O 51411

A star s color gives an indication of its temperature and age The chart shows seven types of stars and th lowest recorded temperature of each type Type A B F G KM P Lowest Temperature in Fahrenheit degrees 1 35 x 104 2 08 x 104 1 08 x 104 9 0 10 6 3 x 10 5 4 x 10 4 5 x 104 Color Blue White Blue White Yellow Orange Red Blue Which type of star has the lowest temperature OP OG COM B

Write the decimal that means the same as 3 321 x 105

Which number below is written in scientific notation 044 2 x 105 00 442 106 04 42 x 107 4 42 x 100 08

A piece of paper has a thickness of 4 2 x 10 inch Which decimal is equivalent to 4 2 10 0 00042 0 042 00 42 0 0042

The planet Mercury is approximately 36 000 000 miles from the sun Which is the distance written in scientific notation 03 6 106 36 x 107 36 x 106 03 6 107

Rewrite this number in standard decimal notation without the use of exponents or scientific notation 2 366 x 104 answer Answers may be entered with or without commas but answers must be exact no rounding at all

Convert the following two numbers to standard notation 2 9 10 3 9 x 10 Convert the following two numbers to scientific notation To enter 2 x 105 you d type 2 10 5 43000 0 00045 Question Help Video Morrago in

Rewrite this number in appropriate scientific notation 328 000 answer

Rewrite this number as a whole number or decimal 6 7 x 105 answer

ewsletter publisher believes that 63 of their readers own a Rolls Royce A testing firm believes this is inaccurate and performs a test to dispute the publisher s m After performing a test at the 0 10 level of significance the testing firm fails to reject the null hypothesis at is the conclusion regarding the publisher s claim swer O There is sufficient evidence at the 0 10 level of significance that the percentage is not 63 O There is not sufficient evidence at the 0 10 level of significance that the percentage is not 63 Tables Keyp Keyboard Shor

O STATISTICS Choosing a quadratic model and usin 2500 2000 The data points show an ocean trench s depth y in feet at a distance x from a marked buoy in feet Each figure has the same data points However each figure has a different curve fitting the data The equation for each curve is also shown Answer the questions that follow 1500 1000 500 Figure 1 y 0 37x 55 6x 305 1 2500 2000 1500 1000 500 Figure 2 y 0 22x 20x 300 2500 X 2000 1500 1000 0 5 500 Figure 3 a Which curve fits the data best O Figure 1 O Figure 2 O Figure 3 b Use the equation of the best fitting curve from part a to predict the depth of the trench 60 feet from the buoy Give an exact answer not a rounded approximation feet Sierra V S Espa ol y 0 12x 4 1x 2 5 H6

A sample of 1100 computer chips revealed that 26 of the chips fail in the first 1000 hours of their use The company s promotional literature claimed that less than 29 fail in the first 1000 hours of their use Is there sufficient evidence at the 0 05 level to support the company s claim State the null and alternative hypotheses for the above scenario Answer Ho Keypad Keyboard Shortcuts Tables

ev The National Academy of Science reported that 32 of research in mathematics is published by US authors The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 32 He has no indication of whether the percentage has increased or decreased since that time He surveys a simple random sample of 295 recent articles published by reputable mathematics research journals and finds that 114 of these articles have US authors Does this evidence support the mathematics chairperson s claim that the percentage is no longer 32 Use a 0 05 level of significance Step 3 of 3 Draw a conclusion and interpret the decision Answer 2 Points Keypad Keyboard Shortcuts We fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0 05 level of significance that the percentage of research in changed mathematics published by US authors We reject the null hypothesis and conclude that there is sufficient evidence at a 0 05 level of significance that the percentage of research in mathematics published by US authors has changed We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0 05 level of significance that the percentage of research in mathematics published by US authors has changed We reject the null hypothesis and conclude that there is insufficient evidence at a 0 05 level of significance that the percentage of research in d by authors has changed N

rev The National Academy of Science reported that 32 of research in mathematics is published by US authors The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 32 He has no indication of whether the percentage has increased or decreased since that time He surveys a simple random sample of 295 recent articles published by reputable mathematics research journals and finds that 114 of these articles have US authors Does this evidence support the mathematics chairperson s claim that the percentage is no longer 32 Use a 0 05 level of significance Step 1 of 3 State the null and alternative hypotheses for the test Fill in the blank below Answer 2 Points Ho p 0 32 Ha P 0 32 Keypad Keyboard Shortcuts

N One study claimed that 88 of college students identify themselves as procrastinators A professor believes that the claim regarding college students is too high The professor conducts a simple random sample of 212 college students and finds that 177 of them identify themselves as procrastinators Does this evidence support the professor s claim that fewer than 88 of college students are procrastinators Use a 0 05 level of significance Step 3 of 3 Draw a conclusion and interpret the decision Answer 2 Points Keypad Keyboard Shortcuts We reject the null hypothesis and conclude that there is insufficient evidence at a 0 05 level of significance that fewer than 88 of college students are procrastinators We reject the null hypothesis and conclude that there is sufficient evidence at a 0 05 level of significance that fewer than 88 of college students are procrastinators We fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0 05 level of significance that fewer than 88 of college students are procrastinators We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0 05 level of significance that fewer than 88 of college students are procrastinators N

One study claimed that 88 of college students identify themselves as procrastinators A professor believes that the claim regarding college students is too high The professor conducts a simple random sample of 212 college students and finds that 177 of them identify themselves as procrastinators Does this evidence support the professor s claim that fewer than 88 of college students are procrastinators Use a 0 05 level significance Step 2 of 3 Compute the value of the test statistic Round your answer to two decimal places Answer 2 Points Keypa

Annie is concerned over a report that a woman over age 40 has a better chance of being killed by a terrorist than of getting married A study found that the likelihood of marriage for a never previously wed 40 year old university educated American woman was 2 8 To demonstrate that this percentage is too small Annie uses her resources at the Baltimore Sun to conduct a simple random sample of 473 never previously wed university educated American women who were single at the beginning of their 40s and who are now 45 Of these women 20 report now being married Does this evidence support Annie s claim at the 0 05 level of significance that the chances of getting married for this group is greater than 2 8 Step 1 of 3 State the null and alternative hypotheses for the test Fill in the blank below Answer Ho p 0 028 Ha P 0 028 4 Tables Keypad Keyboard Shortcuts

A direct mail appeal for contributions from a university s alumni and supporters is considered to be too costly if less than 16 of the alumni and supporters provide monetary contributions To determine if a direct mail appeal is cost effective the fundraising director sends the direct mail brochures to a simple random sample of 348 people on the alumni and supporters mailing lists They receive monetary contributions from 43 people Does this evidence demonstrate that the direct mail campaign is not cost effective Use a 0 05 level of significance Step 3 of 3 Draw a conclusion and interpret the decision Answer Tables Keypad Keyboard Shortcuts O We reject the null hypothesis and conclude that there is insufficient evidence at a 0 05 level of significance that the direct mail campaign is not cost effective O We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0 05 level of significance that the direct mail campaign is not cost effective O We reject the null hypothesis and conclude that there is sufficient evidence at a 0 05 level of significance that the direct mail campaign is not cost effective We fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0 05 level of significance that the direct mail campaign is not cost effective

A direct mail appeal for contributions from a university s alumni and supporters is considered to be too costly if less than 16 of the alumni and supporters provide monetary contributions To determine if a direct mail appeal is cost effective the fundraising director sends the direct mail brochures to a simple random sample of 348 people on the alumni and supporters mailing lists They receive monetary contributions from 43 people Does this evidence demonstrate that the direct mail campaign is not cost effective Use a 0 05 level of significance Step 1 of 3 State the null and alternative hypotheses for the test Fill in the blank below Answer Ho p 0 16 Ha P 0 16 Keypad Keyboard Shortcuts Tables

Sleep apnea is a condition in which the sufferers stop breathing momentarily while they are asleep This condition results in lack of sleep and extreme fatigue during waking hours A current estimate is that 9 7 million out of the 312 7 million Americans suffer from sleep apnea or approximately 3 1 A safety commission is concerned about the percentage of commercial truck drivers who suffer from sleep apnea They do not have any reason to believe that it would be higher or lower than the population s percentage To test the claim that the percentage of commercial truck drivers who suffer from sleep apnea is not 3 1 a simple random sample of 406 commercial truck drivers is examined by a medical expert who concludes that 5 suffer from sleep apnea Does this evidence support the claim that the percentage of commercial truck drivers who suffer from sleep apnea is not 3 1 Use a 0 05 level of significance Step 3 of 3 Draw a conclusion and interpret the decision Answer Keypad Keyboard Shortcuts Tables We reject the null hypothesis and conclude that there is sufficient evidence at a 0 05 level of significance that the percentage of commercial truck drivers who suffer from sleep apnea is not 3 1 We reject the null hypothesis and conclude that there is insufficient evidence at a 0 05 level of significance that the percentage of commercial truck drivers who suffer from sleep apnea is not 3 1 We fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0 05 level of significance that the percentage of commercial truck drivers who suffer from sleep apnea is not 3 1 We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0 05 level of significance that the percentage of commercial truck drivers who suffer from sleep apnea is not 3 1 Submit Answer

Sleep apnea is a condition in which the sufferers stop breathing momentarily while they are asleep This condition results in lack of sleep and extreme fatigue during waking hours A current estimate is that 9 7 million out of the 312 7 million Americans suffer from sleep apnea or approximately 3 1 A safety commission is concerned about the percentage of commercial truck drivers who suffer from sleep apnea They do not have any reason to believe that it would be higher or lower than the population s percentage To test the claim that the percentage of commercial truck drivers who suffer from sleep apnea is not 3 1 a simple random sample of 406 commercial truck drivers is examined by a medical expert who concludes that 5 suffer from sleep apnea Does this evidence support the claim that the percentage of commercial truck drivers who suffer from sleep apnea is not 3 1 Use a 0 05 level of significance Step 1 of 3 State the null and alternative hypotheses for the test Fill in the blank below Ho p 0 031 Ha P 0 031

Postpartum depression and anxiety PPD is a common medical condition affecting mothers and their families after the birth of a baby The CDC estimated that 15 of women who have recently given birth suffer from PPD However this research only reflected self reported cases Therefore one group dedicated to helping women and their families with PPD believes that the true percentage of women who suffer from PPD is much higher The group conducts a simple random sample of 108 women who had given birth in the last year and discovers that 23 of them report having PPD Based on this evidence can the group claim that the true percentage of women who have PPD is greater than 15 Use a 0 05 level of significance Step 3 of 3 Draw a conclusion and interpret the decision Answer Tables Keypad Keyboard Shortcuts We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0 05 level of significance that the true percentage of women who have PPD is greater than 15 We fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0 05 level of significance that the true percentage of women who have PPD is greater than 15 We reject the null hypothesis and conclude that there is sufficient evidence at a 0 05 level of significance that the true percentage of women who have PPD is greater than 15 We reject the null hypothesis and conclude that there is insufficient evidence at a 0 05 level of significance that the true percentage of women who have PPD is greater than 15

1 How many outcomes are in the event B A Answer B

Postpartum depression and anxiety PPD is a common medical condition affecting mothers and their families after the birth of a baby The CDC estimated that 15 of women who have recently given birth suffer from PPD However this research only reflected self reported cases Therefore one group dedicated to helping women and their families with PPD believes that the true percentage of women who suffer from PPD is much higher The group conducts a simple random sample of 108 women who had given birth in the last year and discovers that 23 of them report having PPD Based on this evidence can the group claim that the true percentage of women who have PPD is greater than 15 Use a 0 05 level of significance Step 1 of 3 State the null and alternative hypotheses for the test Fill in the blank below Ho p 0 15 Ha P 0 15 Keypad Keyboard Shortcuts Tables

7 From past experience it is known 90 of 1 year old children can distinguish their mother s voice from the voice of a similar sounding female A random sample of 20 1 year olds is given this voice recognition test 12 points HINT This is a binomial distribution n p q HINT 2 The value of p will change depending on the children recognizing or the children not recognizing the voice A Find the probability at least 3 children do not recognize their mother s voice B Find the probability all 20 children recognize their mother s voice I C Find the mean and standard deviation of x where x is the random variable denoting the number of children who recognize their mother s voice D Find the probability that at most 4 children recognize their mother s voice

A publisher reports that 44 of their readers own a particular make of car A marketing executive wants to test the claim that the percentage is actually different from the reported percentage A random sample of 260 found that 40 of the readers owned a particular make of car State the null and alternative hypotheses Answer Ho Tables Keypad Keyboard Shortcuts

I 1 75 Multiple Choice 3 points each The expected number of 1 s or 2 s in 240 rolls of a six sided die is a 60 a 50 15 b 40 2 The standard deviation of a binomial distribution for which n 50 and p 0 15 is a 0 599 b 7 082 a 2 5 c 80 b 0 914 3 If the random variable x is binomially distributed with n 10 and p 0 05 then P x 2 is c 6 375 b 0 0821 d 120 c 0 074 d 2 525 4 Given a Poisson random variable x where the average number of times an event occured in a certain period of time is 2 5 then P x 0 is c 1 5811 d 0 55 d 0 40 Which of the following experiments can be modeled by the Poisson distribution a The number of calls received by a switchboard in 1 hour b The number of bacteria per 22 ml of fluid c The number of customer arrivals at a checkout counter in 1 day d All of the above

The National Academy of Science reported that 33 of research in mathematics is published by US authors The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 33 He has no indication of whether the percentage has increased or decreased since that time He surveys a simple random sample of 280 recent articles published by reputable mathematics research journals and finds that 108 of these articles have US authors Does this evidence support the mathematics chairperson s claim that the percentage is no longer 33 Use a 0 01 level of significance Step 3 of 3 Draw a conclusion and interpret the decision Answer Tables Keypad Keyboard Shortcuts We reject the null hypothesis and conclude that there is sufficient evidence at a 0 01 level of significance that the percentage of research in mathematics published by US authors has changed O We fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0 01 level of significance that the percentage of research in mathematics published by US authors has changed We reject the null hypothesis and conclude that there is insufficient evidence at a 0 01 level of significance that the percentage of research in mathematics published by US authors has changed We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0 01 level of significance that the percentage of research in mathematics ublished by US authors has changed

12 In a food processing and packaging plant there are on the average two packaging machine breakdowns per week Assume the weekly machine breakdowns follow a Poisson distribution 10 points A Find the mean and standard of this distribution B Find the probability that there are no machine breakdowns in a given week C Find the probability that there are no more than two machine breakdowns in a given week I D Find the probability that there are 3 or more machine breakdowns in a given week

1 75 6 Let x denote the number of cars sold at Hatton Ford during a given week and p x is the probability that x occurs Complete the table to answer the questions that follow 11 points X 0 1 234 5 TOTALS p x 06 12 20 25 30 07 x p x x p x A Find the average number of cars sold in any given week B Find the variance and the standard deviation of the number of cars sold C Find each listed probability 1 P x 4 2 P 0 x 3 3 P 0 x 5

D Find the probability that at most 4 children recognize their mother s voice 8 Consider an experiment with 25 trials where the probability of success on any trial is 0 04 and let the random variable x be the number of successes among the 25 trials Find each probability listed below 11 points A P x 0 B P x 1 C P x 2 D P x 3 X E Explain how you could use the answers from A D to determine P x 4 p q n

9 The number of telephone calls coming into a business s switchboard averages 4 calls per minute Let x be the number of calls received 10 points A This is a B Find P x 0 distribution C Find the probability there will be at least 1 call a given 1 minute period D Find the probability there will be exactly 4 calls in a given 1 minute period E Calculate the mean and standard deviation for x the number of call received per minute at this switchboard

11 From a group of 10 bank officers 3 are selected to be relocated and supervise new branch offices If two of the 10 officers are women and 8 are men what is the probability exactly one of the officers to be relocated will be a woman 6 points A This is a B r b n distribution C Answer the question posed above X

The National Academy of Science reported that 33 of research in mathematics is published by US authors The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 33 He has no indication of whether the percentage has increased or decreased since that time He surveys a simple random sample of 280 recent articles published by reputable mathematics research journals and finds that 108 of these articles have US authors Does this evidence support the mathematics chairperson s claim that the percentage is no longer 33 Use a 0 01 level of significance Step 1 of 3 State the null and alternative hypotheses for the test Fill in the blank below Ho p 0 33 Ha P 0 33

13 A new surgical procedure is said to be successful 80 of the time Suppose the operation is performed five times and the results are assumed to be independent of one another 12 points A List the values A may take on B p q n C What is the probability that all 5 operations are successful D What is the probability exactly 4 are successful E What is the probability that less than 2 are successful A F If less than 2 operations were successful how would you feel about the performance of the surgical team Explain

10 Suppose that the probability that an adult in America will watch the upcoming World Series is 40 Each person is considered independent We are interested in the number of adults in America we must survey until we find one who will watch the World Series 10 points A This is a B List the values that X may take on C How many adults in America do you expect to survey until you find one who will watch the World Series distribution p VD Find the probability that you must ask 7 people I E Find the probability that you must ask 3 or 4 people