A retailer claims that 90% of its customers are "pleased" or "very pleased" with the customer service. In a survey of 300 customers taken last week, what is the probability that 84% or more will be "pleased" or "very pleased" with the service?
A) 0.1736
B) 0.5736
C) 0.3464
D) Almost 100%
E) Almost no chance

Question

Quizplus · Accepted Answer

Given the retailer's claim that 90% of its customers are pleased, the probability of a customer being pleased or very pleased is quite high. For a sample size of 300, the expected number of pleased customers is 270 (90% of 300). The question asks for the probability of 84% or more being pleased, which translates to 252 or more customers out of 300. Given the large sample size and the high percentage of satisfaction, the probability of at least 84% of customers being pleased is very high, approaching almost 100%. This is because the sample proportion is very likely to be close to the population proportion (90%) due to the law of large numbers.

A Retailer Claims That 90% of Its Customers Are "Pleased