Statistics Questions and Answers

The distribution of the ages of of all IRSC students is known to be normally distributed with a mean of 23 0 years and a standard deviation of 4 6 years Use this information to determine the following probabilities Round solutions to four decimal places if necessary Find the probability that a random sample of 66 students has a mean age of greater than 24 8 years P 24 8 Find the probability that a random sample of 66 students has a mean age between 21 5 and 23 6 y 5 years P 21 5 23 6

The indicated function y x is a solution of the associated homogeneous equation Use the method of reduction of order to find a second solution y x of the homogeneous equation and a particular solution y x of the given nonhomogeneous equation y 7y 6y x Y ex X2 x Yp x

Question 1 here are 5 important assumptions associated with sumption identify the most important consequen sumption ansect lines are randomly located organisms located directly on the Initial distribut Choose Initial distributi E

7 uation best describes the relat

nd the largest interval centered about x 0 for which the given initial value problem has a unique solution Enter your answer using interval notation y tan x y ex y 0 1 y 0 0

The given two parameter family is a solution of the indicated differential equation on the interval Determine whether a member of the family can be found that satisfies the boundary conditions If yes enter the solution If an answer does not exist enter DNE y c e cos x c ex sin x y 2y 2y 0 a y 0 1 y 0 y b y 0 1 y 1 y c y 0 1 y 2 1 y d y 0 0 y 0 y

O The mean will be roughly equal to the median O None of the above O The mean will be higher than the median O The median will be higher than the mean Question 45 Which of the following is true if the distribution of scores is positively skewed O The mean will be higher than the median O The mean will be equal to the median O The median will be higher than the mean

What is the median score on this quiz 03 00 O There is no median score 01 04 02 Question 37 The letter grades on a final exam are A A B B B B C D D D F F What is the modal score on this exam OD OB

Which of the following best describes what a unimodal distribution is OTwo or more large bumps O Negatively skewed O One large bump Positively skewed

If a researcher sets out to examine whether better high school performance is related to higher income after high school which is the independent variable O High school performance Education level O Working high school students O Income after high school

LT HIGH SCHOOL HIGH SCHOOL GRADUATE SOME COLLEGE ASSOCIATE S DEGREE BACHELOR S DEGREE GRADUATE DEGREE Total Frequency Percent Valid 36 177 79 74 105 29 500 7 20 35 40 15 80 14 80 21 00 5 80 100 00 7 20 35 40 15 80 14 80 21 00 5 80 100 00 O There are five hundred people in the population that we want to generalize to Bachelor s degrees are the rarest level of education in this population About 16 of the population has an associate s degree Cumulative 7 20 42 60 58 40 73 20 94 20 100 00

The Thomas Supply Company Inc is a distributor of gas powered generators As with any business the length of time customers te to pay their invoices is important Listed below arranged from smallest to largest is the time in days for a sample of the Thomas Supply Company Inc invoices 13 13 13 20 26 26 28 41 41 41 42 43 45 47 Click here for the Excel Data File Round your answers to 2 decimal places a Determine the first and third quartiles First quartile Third quartile 32 00 48 00 Second decile Eighth decile 31 34 34 48 49 b Determine the second decile and the eighth decile 27 00 51 00 35 55 35 38 36 37 56 62 67 82

Caleb inspects a batch of products by sampling 4 of them without replacement If at least one of the products is defective in the sample the whole batch is sent back Caleb doesn t know it but in the batch he is inspecting now there are 100 products and 16 are defective If he samples 4 products from this batch without replacement what is the probability that a All of the products in the sample will be defective b None of the products in the sample are defective c At least one of the products is defective and the whole batch is sent back For all of the above round to three decimal places

Lacy draws a club from a standard deck of 52 cards Without replacing the first card she then proceeds to draw a second card and gets a spade Are these events independent Input Yes or No Determine the probability of drawing a club and then a spade without replacement Write your answer in decimal form rounded to four decimal places as needed Answer Linda draws a club from a standard deck of 52 cards She returns the club to the deck then draws a second card Her second card is a spade Are these events independent Input Yes or No Determine the probability of drawing a club and then a spade with replacement Write your answer in decimal form rounded to four decimal places as needed Answer

A company estimates that 0 2 of their products will fail after the original warranty period but within 2 years of the purchase with a replacement cost of 200 If they offer a 2 year extended warranty for 20 what is the company s expected value of each warranty sold Question Help Video Message insta

If the odds against a certain event are 27 to 7 what is the probability of the event occuring Write your answer as a simplified fraction

A bag contains 3 gold marbles 10 silver marbles and 23 black marbles Someone offers to play this game You randomly select one marble from the bag If it is gold you win 3 If it is silver you win 2 If it is black you lose 1 What is your expected value if you play this game

The weatherman says that there is a 88 chance of rain today What is the probability that it will not rain today What are the odds that it will rain today What are the odds that it will not rain today You can retry th to to Simplify your answers and round to the nearest hundredth as needed Question Help Video Message instructor

5 Suppose that 43 of a town s population have blue eyes 46 have blonde hair and 24 have both blue eyes and blonde hair What is the probability that a randomly selected individual in the town will have blue eyes or blonde hair

Lacy draws a 6 from a standard deck of 52 cards Without replacing the first card she then proceeds to draw a second card and gets a 9 Are these events independent Input Yes or No Linda draws a 6 from a standard deck of 52 cards She replaces the first card and proceeds to draw a second card and gets a 9 Are these events independent Input Yes or No

6 sided die rolled twice Let E be the event the first roll is a 4 and F the event the second roll is a 4 a Are the events E and F independent Input Yes or No b Find the probability of showing a 4 on both rolls Write your answer as a reduced fraction Ancurs

In a large population 55 of the people have been vaccinated If 4 people are randomly selected what is the probability that AT LEAST ONE of them has been vaccinated Give your answer as a decimal to at least 3 places or fraction

Suppose that 40 of people own dogs If you pick two people at random what is the probability that t both own a dog Give your answer as a decimal to at least 3 places or fraction

A 40 year old man in the U S has a 0 244 risk of dying during the next year An insurance company charges 260 per year for a life insurance policy that pays a 100 000 death benefit What is the expected value for the person buying the insurance Round your answer to the nearest dollar Expected Value for the year

An American roulette wheel has 38 slots 18 red 18 black and 2 green What are the odds for the ball landing in a green slot to What are the odds aganst the ball landing in a green slot to

The probability that event A will occur is P A 0 32 What is the probability in decimal form that event A will not occur P A What are the odds for event A What are the odds against event A to to

Find the indicated probability Empirical evidence shows that the normal resting ac normally distributed with a mean of 98 2 degrees Fah deviation of 0 7 degrees Fahrenheit What is the probability that a randomly selected adul temperature that is less than 99 degrees Fahrenheit 0 95 auto d2l ou 341276 ispry c 0 84 087

a the indicated area Find the area of the indicated region under the sta 0 0606 0 0574 0 1 50 2 50

Question 20 1 point Find the indicated probability A battery company has found that the defect Each day 7 batteries are randomly tested Fin to be defective 0 257 035

Find the indicated probability The CDC estimates that 75 of children betwe vaccination If 7 children within this age group probability that more than 5 of them have rece 0 444 0 556 0 25 0 311

uestion 27 1 point Identify the data value corresponding to the indic The length of human pregnancies from conception distribution that is approximately normal with a m deviation of 16 days How long do the longest 5 of pregnancies last 268 or more days

estion 30 1 point terpret the median study of unemployment rates in all 50 s ate of 8 Half of the 50 states had an unemplo The average unemployment rate of th

uestion 14 1 point Select the most appropriate response The average percentage of correct responses on th with a standard deviation of 6 What can be said about a particular student s perc wo The student earned a 78

5 Solve the following LP problem using Dual SA Minimize g x1 x2 x3 5x1 x2 2x3 subject to 2x x3 0 X1 X 1 X2 3x1x x3 3

Based on your answers for the mean and standard deviation found in Question 8 determine the Range Rule of Thumb for the number of people infected with this new disease among 2600 people Use the Range Rule of Thumb to answer the following question Is it unusually high to have 450 people infected with the new disease Please answer the question using a complete sentence For full credit please type out your calculations in the space below Round your answer to the nearest tenth Remember to include your units

Group A Group B Results of a test administered to two groups of people 245 32 Passed 55 18 Failed Use the made up data about results of a test administered to two groups of people to answer all of the following four questions For full credit please type out in the space below the probability statement the set up for your calculations and the answer for each of the questions In your work please indicate clearly which question you are answering 1 If one subject is randomly selected find the probability that she he is from Group B or failed the test 2 If three different subjects are randomly selected find the probability that all three individuals failed the test and were from Group A 3 If six subjects are randomly selected with replacement find the probability that all six individuals passed the test and were from Group A 4 If one subject is randomly selected find the probability that the person failed the test given that she he was from group B

6 16 Is college four year college degree and are not currently enrolled in school 48 said they decided not to go to college because they could not afford school a A newspaper article states that only a minority of the Americans who decide not to go to college do so because they cannot afford it and uses the point estimate from this survey as evidence Conduct a hypothesis test to determine if these data provide strong evidence supporting this statement The hypotheses for this test are Ho p 5 Ha p 5 O Ho p 5 Ha p 5 Ho p 5 Ha p 5 The test statistic is 0 7277 with this hypothesis test is conclusion of the hypothesis test please round to 4 decimal places The p value associated x please round to 4 decimal places What is the O Since p a we reject the null hypothesis and accept the alternative Since p a we reject the null hypothesis and accept the alternative O Since p a we accept the null hypothesis Since p a we fail to reject the null hypothesis Since p a we do not have enough evidence to reject the null hypothesis

Precipitation cm 400 38 0 16 0 340 32 0 300 280 26 0 240 220 200 18 0 160 14 0 12 0 100 8 0 60 40 2 0 60 Climograph I ON xxx 0 Temperature c Precipitation cm 40 0 38 0 36 0 14 0 32 0 30 0 28 0 26 0 24 0 22 0 20 0 18 0 16 0 14 0 12 0 100 80 60 40 2 0 10 0 Climograph J Month Month Figure 9 9 Climograph Examples 1 on left and J on right 151 Pin It The Five Main Controls on Temperature Remember the five climatic controls when analyzing a location s climate latitude continentality wind patterns and air masses ocean currents and elevation N 8 Apply What You Learned Match climographs B through J shown in Figures 9 4 9 5 9 6 9 8 and 9 9 above to their real world locations shown in Table 9 2 To complete Table 9 2 use a globe atlas or the Internet to find where each city is located the city s elevation and whether the city is maritime coastal or continental inland of a continent Tips 32 Temperature in

A mortgage company shows its rates for 30 year fixed rate mortgages from 197 y Year 1975 1980 1985 1990 1995 2000 2005 2010 r Mortgage rate 9 05 13 74 12 43 10 13 7 93 8 05 5 87 4 69 In the blank provied provide two pieces of information explain in practical torm

For questions 9 10 use the random numbers given and the information in the question to assign numbers and estimate the probability of making two free throws in a row 2934 8751 1177 7333 0426 6954 3475 Answer choices Make 00 75 miss 76 99 Make 00 74 miss 75 99 Make 76 99 miss 00 75 Make 75 99 miss 00 74 5452 5635 9523 9 There is a 75 chance of Derrick making a free throw Assign digits to make free throw and miss free throw If we were to use two digits to represent each which of the following would be a correct method of assigning these digits 3326 6957 7634 0438 2045 0 55 0 65 0 75 0 85 3980 Answer choices 6153 1617 5296 10 Use the random numbers to estimate the probability that Derrick makes two free throws in a row The first two digits represent the first free throw and the second two represent the second throw 0902

The pmf of the amount of memory X GB in a purchased flash drive is given as the following 2 4 8 16 p x 0 05 0 20 0 25 0 30 0 20 X 1 a Compute E X in GB Enter your answer to two decimal places 7 05 GB b Compute V X in GB2 directly from the definition Enter your answer to four decimal places 5 11 X GB2 2 26 c Compute the standard deviation of X in GB Round your answer to three decimal places X GB 5 11 d Compute V X in GB2 using the shortcut formula Enter your answer to four decimal places

A small market orders copies of a certain magazine for its magazine rack each week Let X demand for the magazine with the following pmf X p x 2 3 1 5 4 1 16 16 16 16 1 4 5 6 3 2 16 16 Suppose the store owner actually pays 2 00 for each copy of the magazine and the price to customers is 4 00 If magazines left at the end of the week have no salvage value is it better to order three or four copies of the magazine Hint For both three and four copies ordered express net revenue as a function of demand X and then compute the expected revenue What is the expected profit if three magazines are ordered Round your answer to two decimal places What is the expected profit if four magazines are ordered Round your answer to two decimal places How many magazines should the store owner order O 3 magazines

A chemical supply company currently has in stock 100 lb of a certain chemical which it sells to customers in 7 1b batches Let X the number of batches ordered by a range suppose that X has the following pmf X p x Compute E X and V X E X V X 1 0 3 batches batches2 2 0 5 3 0 1 4 0 1 Compute the expected number of pounds left after the next customer s order is shipped and the variance of the number of pounds left Hint The number of pounds left is a linear function of X expected weight left lb 16 variance of weight left

A mail order company business has six telephone lines Let X denote the number of lines in use at a specified time Suppose the pmf of X is as given in the accompanying table 0 1 2 3 4 5 6 p x 0 11 0 15 0 20 0 25 0 19 0 09 0 01 X Calculate the probability of each of the following events a at most three lines are in use b fewer than three lines are in use c at least three lines are in use d between two and five lines inclusive are in use e between two and four lines inclusive are not in use f at least four lines are not in use

Another possibility would be to use a lottery to generate a single priority list and then apply the over and above processing rule Based on the application statistics from the previous question 483 927 applications of which 150 017 were reserve eligible if the US had used this system single lottery over and above for FY 2023 how many advanced degree holders would be expected to receive visas Tyne your answer

Say that a selection rule respects the spirit of affirmative action if making an applicant reserve eligible can NEVER cause them to lose a spot that they otherwise would have received That is a selection rule respects the spirit of affirmative action if for EVERY set of inputs i ii iii above and EVERY applicant who receives a position and is not reserve eligible this applicant would continue to receive a position if they became reserve eligible holding all other inputs fixed Consider the selection rule described by the following procedure take the R highest priority reserve eligible applicants and the U highest priority applicants who are not reserve eligible Call this the separate quotas selection rule Does the separate quotas rule respect the spirit of affirmative action Justify your opcwor

Many investors and financial analysts believe the Dow Jones Industrial Average DJIA gives a good barometer of the overall stock market On January 31 2006 9 of the 30 stocks making up the DJIA increased in price The Wall Street Journal February 1 2006 On the basis of this fact a financial analyst claims we can assume that 30 of the stocks traded on the New York Stock Exchange NYSE went up the same day A sample of 73 stocks traded on the NYSE that day showed that 11 went up You are conducting a study to see if the proportion of stocks that went up is is significantly less than 0 3 You use a significance level of a 0 001 What is the test statistic for this sample Use p rounded to 4 decimal places Report answer accurate to 4 decimal places test statistic What is the p value for this sample Report answer accurate to 4 decimal places p value

Next question You can retry this question below 6 18 Is college worth it Part II Exercise 6 16 presents the res who decide to not go to college do so because they cannot affo a Calculate a 90 confidence interval for the proportion of An because they cannot afford it and interpret the interval in con lower bound x please round to f x please round to f upper bound confidence interval in context We can be 90 confident that our confidence interval com who choose not to go to college because they cannot affo We can be 90 confident that the proportion of American they cannot afford it is contained within our confidence i O 90 of Americans choose not to go to college because the

6 16 Is college worth it Part I Among a simple random sample of 331 American adults who do not have a four year college degree and are not currently enrolled in school 48 said they decided not to go to college because they could not afford school a A newspaper article states that only a minority of the Americans who decide not to go to college do so because they cannot afford it and uses the point estimate from this survey as evidence Conduct a hypothesis test to determine if these data provide strong evidence supporting this statement The hypotheses for this test are O Ho p 5 Ha p 5 O Ho p 5 Ha p 5 O Ho p 5 Ha p 5 The test statistic is this hypothesis test is please round to 4 decimal places The p value associated with please round tod decimal

You are concerned that nausea may be a side effect of Tamiflu but you cannot just give Tamiflu to patients with the flu and say that nausea is a side effect if people become nauseous This is because nausea is common for people who have the flu From past studies you know that about 31 of people who get the flu experience nausea You collected data on 1708 patients who were taking Tamiflu to relieve symtoms of the flu and found that 582 experienced nausea Use a 0 01 significance level to test the claim that the percentage of people who take Tamiflu for the relief of flu symtoms and experience nausea is greater than 31 a Identify the null and alternative hypotheses Ho H b What type of hypothesis test should you conduct left right or two tailed Oleft tailed Oright tailed Otwo tailed c Identify the appropriate significance level d Calculate your test statistic use p rounded to 4 decimal places Round your test statistic to 4 decimal places e Calculate your p value and round to 4 decimal places