The manager for State Bank and Trust has recently examined the credit card account balances for the customers of her bank and found that 20% have an outstanding balance at the credit card limit. Suppose the manager randomly selects 15 customers and finds 4 that have balances at the limit. Assume that the properties of the binomial distribution apply. What is the probability of finding 4 customers in a sample of 15 who have "maxed out" their credit cards?
A) 0.1876
B) 0.8358
C) 0.6482
D) 0.3832

Question

Quizplus · Accepted Answer

The probability can be calculated using the binomial probability formula, which is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials (15 customers), k is the number of successes (4 customers with maxed out credit cards), and p is the probability of success on a single trial (20% or 0.20). Plugging these values into the formula gives the probability of finding exactly 4 customers with maxed out credit cards, which matches choice A.

The Manager for State Bank and Trust Has Recently Examined