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 that 4 or fewer customers in the sample will have balances at the limit of the credit card?
A) 0.1876
B) 0.8358
C) 0.6482
D) 0.3832

Question

Quizplus · Accepted Answer

The probability of 4 or fewer customers having balances at the limit can be calculated using the cumulative binomial probability formula, which sums the probabilities of 0, 1, 2, 3, and 4 customers having balances at the limit. Given the success probability of 0.20 (20%) and a sample size of 15, the cumulative probability of observing 4 or fewer successes (customers at their limit) is closest to the option B) 0.8358. This calculation involves summing the individual binomial probabilities for 0 through 4 successes, which aligns with the properties of the binomial distribution.

The Manager for State Bank and Trust Has Recently Examined