Question

Dorothy Little purchased a mailing list of 4,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list. She randomly selects eight names from the list for validation. If 30% of the names on the list are non-authentic, and x is the number of non-authentic names in her sample, P( x < 2) is ______________.

Answer 1

Answer:

The probability that in a sample of 8 names less than 2 are non-authentic is 0.26

Step-by-step explanation:

The random variable X is defined as the number of non-authentic names on the list.

It is provided that the proportion of non-authentic names on the list is, p = 0.30.

Dorothy selects a random sample of size, n = 8.

The random variable X follows a Binomial distribution with parameters n = 8 and p = 0.30.

The probability mass function of a Binomial distribution is:

$P(X=x)={n\choose x}p^{x}(1-P)^{n-x};\ x=0, 1, 2,...$

Compute the probability that in a sample of 8 names less than 2 are non-authentic as follows:

P (X < 2) = P(X = 0) + P (X = 1)

              $={8\choose 0}(0.30)^{0}(1-0.30)^{8-0}+{8\choose 1}(0.30)^{1}(1-0.30)^{8-1}\\=(1\times1\times0.0576)+(8\times0.30\times0.0824)\\=0.25536\\\approx0.26$

Thus, the probability that in a sample of 8 names less than 2 are non-authentic is 0.26.