A questionnaire study was conducted and it was observed that the \"activity\" th

Question

A questionnaire study was conducted and it was observed that the "activity" that airline passengers like to engage in the most is to sleep. In fact, 60% of respondents to a survey chose this activity over others. For the purposes of this problem, assume the survey respondents came from a random sample of all airline passengers. Now, assume we speak to 10 random people from this population who are just about to board a large flight, and we know that these people do not know one another. Let X = the number of people from these 10 who say they would, of all activities, prefer to sleep on the plane. Here, then, we can assume X ~ Binom(n = 10, p=.60). What is P(X = 6) and P(X = 6)" ?

Explanation / Answer

We use the binomial pdf function to solve the problem:

P(n,p,x) = P(10, .60, 6) = nCx (p^x)(1-p)^n-x

Hence, we have:

P(X=6) = 10C6(.6^6)(.4^4) = 0.25082

P(X=6)c = 1- P(X=6) = 1-0.25082 = 0.74918

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