Albert Abbasi,VP of Operations at Ingleside International Bank,is evaluating the service level provided to walk-in customers. Accordingly,he plans a sample of waiting times for walk-in customers. If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes,the probability that Albert's sample of 64 will have a mean less than 14 minutes is ________.
A) 0.4772
B) 0.0228
C) 0.9772
D) 0.9544
E) 1.0000

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the central limit theorem. According to this theorem, if the sample size is large enough (generally, n ≥ 30), then the distribution of the sample means will be approximately normal, regardless of the shape of the population distribution.

In this case, n = 64, which is greater than 30. So we can use the normal distribution to approximate the sampling distribution of the mean waiting time.

The z-score corresponding to a sample mean of 14 minutes is:

z = (14 - 15) / (4 / sqrt(64)) = -2

Using the standard normal distribution table, we find that the probability of obtaining a sample mean less than -2 is 0.0228. Therefore, the answer is B: 0.0228.

Albert Abbasi,VP of Operations at Ingleside International Bank,is Evaluating the Service