A study was performed to assess the feasibility of a national random digit diali

Question

A study was performed to assess the feasibility of a national random digit dialing cellular phone survey among young adults age 18-34. It was reported that 3.1% of respondents were eligible to participate and that 52% of eligible respondents agreed to participate.

Suppose 1000 potential participants are contacted to participate in the survey. What is the probability that at least 10 of the 1000 participants will be eligible and agree to participate? Hint: Use a computer program to answer this question.

Explanation / Answer

Probability that an individual from 1000 participants will be eligible and agree to participate in a survey, p = 0.031*0.52 = 0.0161

Now this problem can be solved using binomial distribution with p = 0.0161

P(X<=9) = BINOM.DIST(9,1000,0.0161,TRUE)

This is an excel formula which gives probability that less than 10 will be eligible and agree to participate in a survey

solving this gives P(X<=9) = 0.0396

Required probability that at least will be eligible and agree to participate in a survey, 1 - P(X<=9) = 1 - 0.0396 = 0.9604

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