# Probability Questions and Answers

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ProbabilityLet s practice more examples Decide if each statement is true or false and then exp your reasoning Expression 5 3 12 8i 6i is equivalent to 9 2i Subtract distribute the negative 6 51 15 9i 1 is equivalent to 10 8i 7 1 121 3 bi 2 7i b 5 would make the equation true 8 i 1 3 31 271 Select One True False True False True False True False True False I think so because 3 12 Y 161 9 21

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ProbabilityYea r 0 1 2 3 4 5 7 Eleven RM 35 000 12 500 10 000 8 500 5 000 8 000 Speedmart RM 35 000 8 000 8 000 8 000 8 000 8 000

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Probabilitypolling booth Sprobability that is the muld be askied before you can find of people eatiting from and asking drom If they voted independently In a Suney them 6 that a person reted independently is 00 probability that is people must Speople who voted independent from a polling The

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Probability888 A pair of dice are rolled a How many total outcomes are possible b List the set of outcomes that make up the event a sum of nine rolled c What is the probability of a sum of nine being rolled

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ProbabilityIf I go to Subway I have a choice of 7 different kinds of bread 13 different meats and 4 kinds of cheese If I always get one bread one meat and one cheese how many different sandwiches can I get

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ProbabilityQuestion 11 3 points 44 of AN N ve of 5 3 Find the following Probability P not a 5

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ProbabilityQuestion 9 4 points HALLE 64 of f 64 54 of off 34 44 54 of of 66 88 69 59 30 49 MS 29 A 90 84 69 54 4 69 30 54 44 20 34 54 A4 34 69 4 54 24 16 Ao 54 104 24 Ao Find the Probability P Five or Black

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Probability7 When Liam commutes to work the amount of time it takes him to arrive is normally distributed with a mean of 55 minutes and a standard deviation of 4 5 minutes a What percentage of times does it take him LESS THAN 60 minutes to get to work 60 55 86 43 2 4 5 578 8643 1 11 b What percentage of times does it take him BETWEEN 46 and 46 55 4 5 2 86 43 2 28 84 15 d What times mark the middle 80 of the commute times e 505 55 59 5 64 68 5 02 28 c Out of the 207 days that Liam commutes to work per year how many times would his commute be between 46 and 60 minutes to the nearest whole number 0 5 207 8415 174 times 10 1 29 x 5S 4 5 4 5 4 5 49 15 60 805 0 5 TOO 80 20 2 10 100 10 90 2 9 5565 1 55 10 5 805 FSS 5 60 805 40 29 x 55 4 5 49 195 4 5 5

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ProbabilityQuestion 4 The diameters of screws in a batch are normally distributed with mean equal to 2 10 cm and standard deviation equal to 0 15 cm I a What proportion of screws are expected to have diameters greater than 2 50 cm 10 P b A specification calls for screw diameters between 1 75 cm and 2 50 cm What proportion of screws will meet the specification 15 P

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ProbabilitySolve the compound inequality and give your answer in interval notation 2 6x3 10 44 AND 1x 4 3x 14 4x

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ProbabilityChoose the most appropriate completion of the sentence In order to indicate a strong correlation between variables the correlation coefficient will be O near 10 O near 1 near 1 2 O near 0 O near 1 or 1 O near 1

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ProbabilityYou are performing a right tailed test with test statistic z 1 344 find the p value accurate to 4 decimal places n value

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ProbabilityThe p value for a hypothesis test turns out to be 0 021868 At a 7 level of significance what is the proper decision O Reject Ho O Fail to reject Ho

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ProbabilityYou are performing a hypothesis test of a single population proportion You find out that np is less than five What must you do to be able to perform a valid hypothesis test O Decrease the sample size so that np is less than five O Increase the sample size so that np is greater than five O Decrease the sample size so that np is greater than five O Increase the sample size so that np is less than five

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ProbabilityUse the quadratic formula to solve the equation Be sure to simplify your answers Enter both answers separated by a comma 16x 4 0

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ProbabilityConsider the following probability model associated with the number of raffle tickets purchased by each customer a 0 15 b 0 25 c 0 35 d 0 20 OC OD O A

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ProbabilitySuppose 70 of all adults drink coffee If you were to conduct a simulation involving coffee drinkers and non coffee drinkers which of the following is a valid assignment of digits to represent coffee drinkers a 0 1 2 coffee drinker 3 4 5 6 7 8 9 not a coffee drinker b 0 1 2 3 coffee drinker 4 5 6 7 8 9 not a coffee drinker c 0 1 2 3 4 coffee drinker 5 6 7 8 9 not a coffee drinker d 0 1 2 3 4 5 6 coffee drinker 7 8 9 not a coffee drinker OC OB

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ProbabilityYou play tennis regularly with a friend and from past experience you believe that the outcome of each match is independent For any given match you have a probability of 0 6 of winning The probability that you lose the next two matches is a 0 16 b 0 40 c 0 64 d 0 36 OB OA C

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ProbabilityA statistics teacher states the probability of a surprise quiz on any given day is 0 30 If quizzes are given independently each day what is the probability there will be a surprise quiz on the next two consecutive days a 0 09 b 0 21 c 0 42 d 0 60 O A OB

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ProbabilityA statistics teacher states the probability of a surprise quiz on any given day is 0 30 If quizzes are given independently each day what is the probability there will be a surprise quiz on the next two consecutive days a 0 09 b 0 21 c 0 42 d 0 60 O A OB

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ProbabilityWhich of the following statements is alse a All possible outcomes together must have probabilities that add up to 1 b An event is random if individual outcomes are uncertain c The probability of any outcome must be a number between 0 and 1 d A probability can be a number greater than 1 OA OD

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ProbabilityWhich of the following statements is alse a All possible outcomes together must have probabilities that add up to 1 b An event is random if individual outcomes are uncertain c The probability of any outcome must be a number between 0 and 1 d A probability can be a number greater than 1 OA OD

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ProbabilitySelect the correct answer for each question s The test pages are attached below for your review All questions may not be listed Chapter 4 Test first 2 pages pdf D Question 1 2 A statistics teacher states the probability of a surprise quiz on any given day is 0 30 If quizzes are gir Independently of the day what is the probability there will be a surprise quiz on the next two consecutive days a 0 09 b 0 21 c 0 42 d 0 60 OA OD

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ProbabilityA student was asked to find a 95 confidence interval for widget width using data from a random sample of size n 29 Which of the following is a correct interpretation of the interval 10 5 p 23 7 Check all that are correct There is a 95 chance that the mean of a sample of 29 widgets will be between 10 5 and 23 7 There is a 95 chance that the mean of the population is between 10 5 and 23 7 With 95 confidence the mean width of all widgets is between 10 5 and 23 7 With 95 confidence the mean width of a randomly selected widget will be between 10 5 and 23 7 The mean width of all widgets is between 10 5 and 23 7 95 of the time We know this is true because the mean of our sample is between 10 5 and 23 7

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ProbabilityIf n 41 42 and s 6 construct a confidence interval at a 80 confidence level Give your answers to one decimal place Technolom

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ProbabilityA student was asked to find a 95 confidence interval for widget width in mm using data from a random sample of size n 18 Which of the following is a correct interpretation of the interval 14 4 p 21 1 Check all that are correct There is a 95 chance that the mean of a sample of 18 widgets will be between 14 4 mm and 21 1 mm The mean width of all widgets is between 14 4 mm and 21 1 mm 95 of the time We know this is true because the mean of our sample is between 14 4 mm and 21 1 mm With 95 confidence the mean width of a randomly selected widget will be between 14 4 mm and 21 1 mm With 95 confidence the mean width of all widgets is between 14 4 mm and 21 1 mm There is a 95 chance that the mean of the population is between 14 4 mm and 21 1 mm

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Probabilitythirty percent of students at a university are business major a random sample of 20 students is selected what is the probability that among the students at least 10 are business major B what is the probability that at least 16 are not business major C what is the probability that exactly 10 are business major D what is the probability that exactly 12are not business majors

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Probabilityvent A Age 12 12 to 15 16 to 24 25 to 64 65 Totals Event B Vaccinated Not Vaccinated 124 873 47 793 946 6 424 266 10 214 213 17 950 590 20 983 450 100 514 773 72 858 178 42 397 381 13 507 909 167 411 883 165 357 696 Totals 47 918 479 16 638 479 38 934 040 173 372 951 55 905 290 332 769 579 Simple Probabilities P Vaccinated P Not Vaccinated P 12 P 12 to 15 P 16 to 24 P 25 to 64 P 65 Joint Probabilities A And B P Vaccinated and 65 P Vaccinated and 12 to 15 P Not Vaccinated and 16 to 24 P Not Vaccinated and 12 Addition Rule A Or B P Vaccinated or 25 P Not Vaccinated or 65 P Vaccinated or 64 P Not Vaccinated or 16 to 24 DINGLY Conditional Probabilities A given B P Vaccinated 12 to 15 P Vaccinated 16 to 24

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Probabilitywent A Age 12 12 to 15 16 to 24 25 to 64 65 Totals Event B Vaccinated Not Vaccinated 124 873 47 793 946 6 424 266 10 214 213 17 950 590 20 983 450 38 934 040 100 514 773 72 858 178 173 372 951 42 397 381 13 507 909 55 905 290 167 411 883 165 357 696 332 769 579 Totals 47 918 479 16 638 479 Simple Probabilities P Vaccinated P Not Vaccinated P 12 P 12 to 15 P 16 to 24 P 25 to 64 P 65 Joint Probabilities A And B P Vaccinated and 65 P Vaccinated and 12 to 15 P Not Vaccinated and 16 to 24 P Not Vaccinated and 12 Addition Rule A Or B P Vaccinated or 25 P Not Vaccinated or 65 P Vaccinated or 64 P Not Vaccinated or 16 to 24 Conditional Probabilities A given B P Vaccinated 12 to 15 P Vaccinated 16 to 24 P Not Vaccinated 65

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ProbabilityMore than 82 of workers got their job through networking Express the null and alternative hypotheses in symbolic form for this claim Ho p HA P

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ProbabilityEvent A Age 12 12 to 15 16 to 24 25 to 64 65 Event B Vaccinated 124 873 6 424 266 17 950 590 100 514 773 42 397 381 Not Vaccinated 47 793 946 10 214 213 20 983 450 72 858 178 13 507 909 Totals

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ProbabilityYou are performing a left tailed test with test statistic z 2 6 find the p value accurate to 4 decimal places p value

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ProbabilityQuestion You Are Considering Buying An Industrial Equipment Whose Price 260000 The You are considering buying an industrial equipment whose price 260000 The equipment is expected to earn an annual revenue of 150 000 The equipment will be depreciated under MACRS as a five year recovery property The equipment will be used for seven years at the end of which time you can sell it for 50 000 Your company s marginal tax rate is 35 over the project period Perform the following a Determine the net after tax cash flows for each period over the project life b Net present worth assuming company MARR 15 c Annual equivalent cash flow company MARR 15 d IRR of the project

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ProbabilityAt most 79 of Internet users pay bills online Express the null and alternative hypotheses ir symbolic form for this claim Ho p O II

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ProbabilityA commonly cited work week hours for an employee is 36 hours A company samples 200 employees and find an average work week hours of 47 hours with a standard deviation of 11 hours Which of the following is the correct set of hypotheses for testing if the average work week hours of an employee of this company is different than the commonly cited standard of 36 hours Ho H 36 HA X 47 Ho H 36 HA 36 HA H 36 Ho x 36 Ho x 47 HA H 36 Ho H 36 HA 36

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ProbabilityA Which of the following could be an equation of the line graphed in the xy plane ab 0y 1 x 1 0y x 1 Oy 2x 1 Oy 2x 1

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ProbabilityA government agency reported that in 2020 6 0 of people with a bachelor s degree and 9 5 of people with a high school diploma but no college were unemployed Suppose that the reported percentages were based on independently selected representative samples of 600 people with a bachelor s degree and 600 people with a high school degree but no college It was also reported that 4 4 of those with master s degrees were unemployed in 2020 Suppose that this reported percentage was based on a representative sample of 250 people with master s degrees Use this information to answer the following questions USE SALT PRACTICE ANOTHER a Construct a 99 large sample confidence interval for the difference in the proportion who were unemployed in 2020 for those who have a bachelor s degree and those who have a master s degree Use Bachelor s Degree Master s Degree Enter your answer using interval notation Round your numerical values to four decimal places X Interpret the interval We are 99 confident degree falls within O that the true difference in the proportion of people with a bachelor s degree who are unemployed and this proportion for people with a master s O this interval The bounds of the interval suggest the two proportions could be equal b The following is a 95 large sample confidence interval for the difference in the proportion who were unemployed in 2020 for those who have a bachelor s degree and those who have a high school diploma but no college 0 0652 0 0048 Is the confidence interval from part a wider or narrower than this confidence interval

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ProbabilityH A report about how American college students manage their finances includes data from a survey of college students Each person in a representative sample of 793 college students was asked if they had one or more credit cards and if so whether they paid their balance in full each month There were 500 who paid in full each month For this sample of 500 students the sample mean credit card balance was reported to be 825 The sample standard deviation of the credit card balances for these 500 students was not reported but for purposes of this exercise suppose that it was 205 Is there convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than 905 the value reported for all college students with credit cards Carry out a hypothesis test using a significance level of 0 01 USE SALT State the appropriate null and alternative hypotheses in dollars Enter for as needed Ho 905 905 AT3 12 3 049 MI S Find the test statistic Round your answer to two decimal places MY NOTES Use technology to find the P value Round your answer to four decimal places P value PRACTICE ANOTHER State the conclusion in the problem context We reject Ho We do not have convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than 905 We fail to reject Ho We do not have convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than 905 We fail to reject Ho We have convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than 905 egree Proje 1 omp RI Biki Fort I Proj S 02

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ProbabilityInsurance 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

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ProbabilityThere 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

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ProbabilityFor 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

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Probabilityhere 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