# Probability Questions and Answers

Statistics

ProbabilityThe time to assemble a product was recorded for each worker at a company in a sample of 30 A 95 confidence interval for u is 149 156 minutes a The individual object in the study was a randomly selected This is computer graded so use exact wording from the problem above b What was the variable information recorded for each object in the study This is computer graded so use exact wording from the problem above c State the statistical interpretation of the confidence interval in the context of this problem Select an answer company is are between the v d What is the symbol and value of the point estimate for u minutes e What is the margin of error for the given interval time to assemble a product of workers at a and minutes f Fill in the boxes below to show the relation on the number line between the numeric values of the point estimate and the interval estimate for A B C

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Probabilityparts a through d a Find the probability of choosing all first shift workers Round to four decimal places as needed b Find the probability of choosing all second shift workers Round to four decimal places as needed c Find the probability of choosing exactly six first shift workers Round to four decimal places as needed d Find the probability of choosing exactly four second shift workers Round to four decimal places as needed

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ProbabilityYou may need to use the appropriate appendix table or technology to answer this question A random sample of 81 credit sales in a department store showed an average sale of 65 00 From past data it is known that the standard deviation of the population is 26 a Determine the standard error of the mean in dollars Round your answer to the nearest cent X 3 b With a 0 95 probability what can be said about the size of the margin of error O There is a 0 95 probability that the distance between the sample mean and the population mean will equal the margin of error O There is a 0 95 probability that the distance between the sample mean and the population mean will be greater than or equal to the margin of error There is a 0 95 probability that the margin of error and the population mean are equal O There is a 0 95 probability that the sample mean and the population mean are equal O There is a 0 95 probability that the distance between the sample mean and the population mean will be less than or equal to the margin of error c What is the 95 confidence interval of the population mean in dollars Round your answers to the nearest cent X 58 9023 X to 71 0977 X

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Probability2 33 The IRS plans an SRS The Internal Revenue Service plans to examine an SRS of individual federal income tax returns from each state One variable of interest is the proportion of returns claiming itemized deduc tions The total number of tax returns in a state varies from almost 30 million in California to approximately 500 000 in Wyoming a Will the margin of error for estimating the popula tion proportion change from state to state if an SRS of 2000 tax returns is selected in each state Explain your answer b Will the margin of error change from state to state if an SRS of 1 of all tax returns is selected in each ver

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Probabilitytep 2 39 Order in choice Does the order in which wine is pre sented make a difference Several choices of wine are pre sented one at a time and in sequence and the subject is then asked to choose the preferred wine at the end of the sequence In this study subjects were asked to taste two wine samples in sequence Both samples given to a subject were the same wine although subjects were expecting to taste two different samples of a particular variety Of the 32 subjects in the study 22 selected the wine presented first when presented with two identical wine samples 29 a Do the data give good reason to conclude that the subjects are not equally likely to choose either of the two positions when presented with two identi cal wine samples in sequence b The subjects were recruited in Ontario Canada via advertisements to participate in a study of at titudes and values toward wine Can we generalize

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Probability1 Running red survey of 880 drivers asked Recalling the last 10 traf fic lights you drove through how many of them were red when you entered the intersections Of the 880 respondents 171 admitted that at least one light had been red 24 a Give a 95 confidence interval for the proportion of all drivers who ran one or more of the last 10 red lights they met b Nonresponse is a practical problem for this survey only 21 6 of calls that reached a live person were completed Another practical problem is that people may not give truthful answers What is the likely direction of the bias do you think more or fewer than 171 of the 880 respondents really ran a red

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Probability25 Do smokers know that smoking is bad for them The Harris Poll asked a sample of smokers Do you believe that smoking will probably shorten your life or not Of the 1010 people in the sample 848 said Yes a Harris called residential telephone numbers at ran dom in an attempt to contact an SRS of smokers Based on what you know about national sample surveys what is likely to be the biggest weakness in the survey b We will nonetheless act as if the people interviewed are an SRS of smokers Give a 95 confidence interval for the percent of smokers who agree tha smoking will probably shorten their lives alessandro0770 Getty Images

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ProbabilityThe pie chart to the right shows how adults rate their financial shape Suppose 18 people are chosen at random from a group of 200 What is the probability that none of the 18 people would rate their financial shape as fair Make the assumption that the 200 people are represented by the pie chart The probability that none of the 18 people would rate their financial shape as fair is Round to six decimal places as needed Excellent 5 Good 44 Fair 36 Poor 13 Other 2

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ProbabilityYou look over the songs in a jukebox and determine that you like 17 of the 55 songs a What is the probability that you like the next four songs that are played Assume a song cannot be repeated b What is the probability that you do not like the any of the next four songs that are played Assume a song cannot be repeated a The probability that you like the next four songs that are played is Round to three decimal places as needed b The probability that you do not like any of the next four songs that are played is Round to three decimal places as needed IDEERI

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ProbabilityA certain lottery has 25 numbers In how many different ways can 5 of the numbers be selected Assume that order of selection is not important There are different ways the numbers can be selected Simplify your answer

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ProbabilityExpress the confidence interval 80 4 8 6 in interval form Express the answer in decimal format do not enter as percents

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Probabilityod and food In a study of the effects of mood on evaluation of nutritious food 208 subjects were ran domly assigned to read either a happy story to induce a positive mood or a control no story neutral mood group Subjects were then asked to evaluate their atti tude toward a certain indulgent food on a nine point scale with higher numbers indicating a more positive attitude toward the food The following table summa rizes data on the attitude rating 14 Group Positive mood Neutral mood n 104 104 X S 4 30 2 05 5 50 1 74 a What are the standard errors of the sample means of the two groups b What degrees of freedom does the conservative Op tion 2 use for two sample t procedures for these data c Test the null hypothesis of no difference between the two group means against the two sided alterna

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Probability11 Weeds among the Corn Lamb s quarter is a common weed that interferes with the growth of corn An agriculture researcher planted corn at the same rate in 16 small plots of ground then weeded the plots by hand to allow a fixed number of lamb s quarter plants to grow in each meter of corn row No other weeds were allowed to grow Here are the yields of corn bushels per acre for only the experimental plots controlled to have one weed per meter of row and nine weeds per meter of row WDCORN One weed meter 166 2 157 3 166 7 161 1 Nine weeds meter 162 8 142 4 162 8 162 4 Explain carefully why a two sample t confidence interval for the difference in

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Probability3 Smart Watch Battery Life To check the lifetime of a new battery in a soon to be released smart watch with GPS an engineer used the GPS tracking fea ture of the watch continuously beginning with a fully charged battery until the battery was drained The engineer repeated this for a total of 10 times He compared the results with the lifetime of 4 8 hours for the current battery used in the company s GPS enabled smart watch

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Probability1 1 Smartphones and Spouses Choose a random sample of 100 married couples Ask each member of the couple how much time they spend looking at their smartphone while at home Compare the mean times for the two mem bers of couples

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Probability1 According to the records of an auto insurance company the average distance that their customers drive to work is 17 4 miles You are a new agent and you think this is too low You do a random polling of 50 of the company s customers and you find that the average is 18 5 miles with a standard deviation of 3 4 miles Do these data provide enough evidence at the 0 05 level of significance to conclude that the average distance driven to work is actually more than 17 4 miles a 1 pt State the null and alternative hypotheses b 1 pt State the p value c 1 pt What is your conclusion about the null hypothesis d 2 pts What is your conclusion in context of this problem

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ProbabilityFind the slope of the line y 8 x 10 Write your answer as an integer or as a simplified proper or improper fraction

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ProbabilityComplete the process of solving the equation Fill in the missing term on each line Simplify any fractions 3y 1 1 3y y Subtract 1 from both sides Divide both sides by 3

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ProbabilityFind the y intercept of the line y 8 13 Write your answer as an integer or as a simplified proper or improper fraction not as an ordered pair

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ProbabilityHere is a sample data set 533 1 619 9 541 2 526 6 434 6 526 6 478 6 539 3 534 4 505 5 431 2 613 4 471 5 541 3 444 6 533 7 468 8 451 9 405 7 538 3 528 9 451 1 549 3 418 2 468 8 518 1 495 8 544 1 468 539 3 631 485 5 483 5 468 8 536 8 472 1 539 1 539 3 608 8 617 7 492 9 509 8 458 1 536 3 531 3 405 4 606 6 526 7 534 2 626 8 440 3 459 6 617 8 500 6 Find the first quartile for this data set Q Find the third quartile for this data set Q3 Find the interquartile range for this data set IQR

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ProbabilityThe percent distribution of live multiple delivery births three or more babies in a particular year for women 15 to 54 years old is shown in the pie chart Find each probability a Randomly selecting a mother 30 39 years old P 30 to 39 b Randomly selecting a mother not 30 39 years old P not 30 to 39 Round to the nearest thousandth as needed c Randomly selecting a mother less than 45 years old P less than 45 Round to the nearest thousandth as needed d Randomly selecting a mother at least 20 years old P at least 20 Round to the nearest thousandth as needed Round to the nearest thousandth as needed SOCCE Number of Multiple Births 00 15 19 1 6 20 24 6 3 25 29 21 3 30 34 37 3 35 39 24 6 40 44 5 3 45 54 3 6

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ProbabilityThe 81 th percentile of lightbulb lifespan is 1500 hours What does this mean of light bulbs have a lifespan of less than or equal to 1500 hours 06 CH

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ProbabilityA set of data items is normally distributed with a mean of 112 and a standard deviation of 15 Convert each of the following data items to a z score Round your answer to the nearest hundredth a 212 Z b 94 Z

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ProbabilityA standard deck of cards contains 52 cards One card is selected from the deck a Compute the probability of randomly selecting a club or diamond b Compute the probability of randomly selecting a club or diamond or heart c Compute the probability of randomly selecting a king or club a P club or diamond Round to three decimal places as needed b P club or diamond or heart Round to three decimal places as needed c P king or club Round to three decimal places as needed

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Probability4 different color dice are rolled and the numbers showing are recorded How many different outcomes are possible Your answer is

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ProbabilityThe Venn diagram here shows the cardinality of each set Use this to find the probability of observing the given set A 5 C 6 7 2 14 8 9 B 4

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ProbabilityA jar contains 5 red marbles numbered 1 to 5 and 10 blue marbles numbered 1 to 10 A marble is drawn at random from the jar Find the probability that the marble is red or odd numbered

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ProbabilityIn how many different ways can a police department arrange a lineup if each lineup contains 8 people

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ProbabilityA survey was conducted at a local ballroom dance studio asking students if they had ever competed in the following dance categories Smooth Rhythm Standard The results were then presented to the owner in the following Venn Diagram Smooth 5 12 15 Standard 6 Rhythm 7 14 a Q If a student is chosen at random what is the probability that Write your answers in percent form Round to the nearest tenth of a percent a The student has competed in none of the categories b The student has competed in all three of these categories c The student has competed in Smooth or Standard but not Rhythm d The student has competed in Rhythm and Standard but not Smooth e The student has competed in Rhythm

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ProbabilityA girl has 8 skirts 9 blouses and 9 pairs of shoes How many different skirt blouse shoe outfits can she wear Assume that each item matches all the others so she is willing to wear any combination Your answer is

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ProbabilityIn the 6 51 lottery game a player picks six numbers from 1 to 51 How many different choices does the player have Your answer is

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ProbabilitySuppose a designer has a palette of 6 colors to work with and wants to design a flag with 3 vertical stripes all of different colors How many possible flags can be created

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ProbabilityIn how many ways can 3 students from a class of 15 be chosen for a field trip Your answer is

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ProbabilityLet P U 0 28 and P V 0 28 and P V 0 47 Events U and V are mutually exclusive Find P U or V O 1 6785714285714 O 0 59574468085106 O 0 75 O 0 1316 O 0 19 O 0 19

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ProbabilityWith a population of 3500 people we randomly sample 139 people without replacement Is it reasonable to assume that the trials are sampled independently O No because the sample size is greater than or equal to 5 of the population size O No because the sample size is less than 5 of the population size O Yes because the sample size is less than 5 of the population size OYes because the sample size is greater than or equal to 5 of the population rito

Statistics

Probabilitythan percents In a family with 5 children what is the probability of having 3 boys and then 2 girls in that order Exclude multiple births and assume all outcomes are equally likely In a family with 5 children what is the probability of having 3 boys and 2 girls in any order Exclude multiple births and assume all outcomes are equally likely

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ProbabilityThe probability that a first year student entering a certain private college needs neither a developmental math course nor a developmental English is 52 while 36 require a developmental math course and 30 require a developmental English course Find the probability that a first year student requires both a development math course and a developmental English course

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ProbabilityYou own 15 CDs You want to randomly arrange 7 of them in a CD rack What is the probability that the ra ends up in alphabetical order The probability that the CDs are in alphabetical order is

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ProbabilityA pianist plans to play 4 pieces at a recital from her repertoire of 23 pieces How many different recital programs are possible

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ProbabilityA restaurant offers a choice of 6 salads 12 main courses and 7 desserts How many possible 3 course meals are there

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ProbabilityStandard automobile license plates in a country display 2 numbers followed by 3 letters followed by 2 numbers How many different standard plates are possible in this system Assume repetitions of letters and numbers are allowed Your answer is

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ProbabilityA die is rolled twice What is the probability of showing a 1 on the first roll and an even number on the second roll Your answer is

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ProbabilityA survey of 138 persons was conducted at TCC and it was found that 10 persons carried a cell phone 97 persons carried a tablet computer and 7 carried both a cell phone and a tablet 1 How many people carried a cell phone or a tablet 2 How many people carried neither a cell phone nor a tablet 3 How many people carried a cell phone only 4 How many people carried a tablet but not a cell phone

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ProbabilityA survey asks Which online services have you used in the last month Twitter Facebook Have used both The results show 33 of those surveyed have used Twitter 59 have used Facebook and 8 have used both What percent of the people surveyed used neither Twitter nor Facebook

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ProbabilityAn urn contains 7 blue 5 yellow and 3 gray marbles Two marbles are randomly drawn from the urn Find the probability the two marbles are the same color O 83 225 O 68 225 O 68 210 03040