Question

Of the population of customers of a store, a proportion of 0.4 are not satisfied with the service
offered by the store. In a random sample of 400 customers, what is the probability that between
156 and 240 customers will be satisfied with the service offered by the store?

Answer 1

Proportion of people who are not satisfied with the service offered = 0.4

Let, p = proportion of people who are satisfied with the service offered

p = 1-0.4 =0.6

Let, x = number of customers who are satisfied

Sample size, n=400

The probability that between 156 and 240 customers will be satisfied with the service offered by the store is equal to

$P(156≤x≤240) = P(\frac{156- (400)(0.6)}{\sqrt{400 \times 0.6 \times 0.4}} ≤ \frac{x-np}{\sqrt{npq}} ≤ \frac{240 -(400)(0.6)}{\sqrt{400 \times 0.6 \times 0.4}}) \\ = P(-8.57 ≤ Z ≤0) \\ =P(Z≤0) -P(Z≤ -8.57) \\ =0.5$