Question

Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list. She randomly selects five names from the list for validation. If 40% of the names on the list are not authentic, and X is the number of non-authentic names in her sample, P(X=0) is (use calculator) a. 0.8154. b. 0.0467. c. 0.0778. d. 0.4000.

Answer 1

Answer: c. 0.0778

Explanation:

Let X is the number of non-authentic names in her sample with parameter :

n= 5 and p=40% = 0.40

Binomial probability distribution, the probability of getting success in x trials :-

`P(X=x)=^nC_xp^x(1-p)^(n-x)`

We have ,

`P(X=0)=^(5)C_0(0.40)^0(1-0.40)^(5)\\\\=(1)(0.60)^(5)\\\\=0.07776\approx0.0778`

Thus , the correct answer is option c. 0.0778