Answer to Question #185101 in Statistics and Probability for Chae

Question

Binomial Distribution

In a survey, 25% of the people interviewed said that they bought their refrigerator during the last six months. If eleven people are selected at random, find the probability that exactly six of these people bought their refrigerator during the last six months.

Answer 1

Let x be a random variable denoting the number of people who bought a refrigerator during the last 6 months.

p=0.25; q=1-p=1-0.25=0.75

Since there are two events, apply the binomial distribution.

$P(X=x) ={n \choose x} p^x q^{n-x}$

When n=11; p(X=6) will be ;

$P(X=6)={11 \choose 6}×0.25^6×0.75^{11-6}$

=0.0268