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# Three couples and two single individuals have been invited

ISBN: 9780321629111 32

## Solution for problem 20E Chapter 3

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 20E

Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is .4 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar. a. ?Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] b.? ?Obtain the cumulative distribution function of X, and use it to calculate P(2? X ? 6).

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Problem 20E Answer: Step1: We have Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is .4 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar. We need to find, a. Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] b. Obtain the cumulative distribution function of X, and use it to calculate P(2 X 6). Step2: Let X be the number of people who arrive late for the seminar. Probability that late arrival of a couple or an individual is 0.4. Probability of arrival on time is 1 - 0.4 = 0.6 We have Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Each individual as two outcomes either comes on late or time. 5 Therefore the total possible outcomes are 2 = 32. a). 1).Consider, X = 0 (when no one is late) P(X = 0) = P(#1)×P(#2)×P(#3)×P(#4)×P(#5) = 0.6×0.6×0.6×0.6×0.6 = 0.07776. 2).Consider, X = 1 (one individual late) So we need to find probability of one P(X = 1) = {[ P(#1)×P(#2)×P(#3)×P(#4)× P(#5)] + [P(#1)×P(#2)×P(#3)× P(#4) ×P(#5)]} = {[0.6×0.6×.06×0.6×0.4] + [0.6×0.6×0.6×.04×0.6]} = {0.05184 + 0.05184} = 0.10368 3).Consider,X = 2 (one couple is late or both individual are late) So we do for one couple and multiply by 3 P(X = 2) = {[P(#1) ×P(#2)×P(#3)×P(#4)× P(#5)]+[P(#1) × P(#2) ×P(#3)×P(#4)× P(#5)]+[P(#1) ×P(#2)× P(#3) ×P(#4)× P(#5)]+[P(#1) ×P(#2)× P(#3) × P(#4) × P(#5)]} = {[0.4×0.6×0.6×0.6×0.6] +[0.4×0.6×0.6×0.6×0.6]+[0.4×0.6×0.6×0.6× 0.6]+ [0.6×0.6×0.6×0.4×0.4]}...

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##### ISBN: 9780321629111

Since the solution to 20E from 3 chapter was answered, more than 1666 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 20E from chapter: 3 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. This full solution covers the following key subjects: late, Couples, Individuals, arrive, Probability. This expansive textbook survival guide covers 18 chapters, and 1582 solutions. The answer to “Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is .4 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar. a. ?Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] b.? ?Obtain the cumulative distribution function of X, and use it to calculate P(2? X ? 6).” is broken down into a number of easy to follow steps, and 123 words.

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Three couples and two single individuals have been invited

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