a journal polled its readers to determine the proportion of wives who, if given

Question

a journal polled its readers to determine the proportion of wives who, if given a second chance, would marry their husband. according to the responses from the survey, 70% of wives would marry their husbands again.suppose a random and independent sample of n=5 wives was collected.define the random variable x as the number of the 5 wives who would marry their husbands again.then we know x is a binomial random variable.find the probability that at most 4 of the wives sampled said they would marry their husbands again.

Explanation / Answer

Define X= the number of the 5 wives who would marry their husbands

Now, X follows binomial distribution with parameters n=5, p=0.70

Find P(at most 4 of the wives sampled said they would marry their husbands again)

=P(X<=4)

=5C0*0.70^0*0.30^1+…+5C4*0.70^4*0.30^1

=0.83193

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