Question

Suppose a random sample of 30 customers is taken to test a company’s claim that 85% of customers are satisfied with their dog food. Assume trials are independent. What is the probability 8 customers aren't satisfied?

Answer 1

Suppose X is a random variable denoting the number of customers who aren't satisfied with the dog food.

Given in a random sample of 30 customers 85% of customers were satisfied with the dog food. Thus, 15% of the customers weren't satisfied with the dog food.

Thus probability that a customer is not satisfied with the dog food is =0.15.

Thus, the preference of the dog food is independent for all customers.

Thus, X~binomial(30, 0.15).

The PMF of X is,

f(x) =³⁰C_x(0.15)^x(0.85)^30-x, x=0, 1,2,...,30.

Therefore, the probability that 8 customers aren't satisfied with the dog food is,

P(X=8) =

=³⁰C₈(0.15)⁸(0.85)²²

=0.042.

Thus, the required probability is, 0.042.