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 closest to________.
A)0.4772
B)0.0228
C)0.9772
D)0.9544
E)1.0000

Question

Quizplus · Accepted Answer

The correct answer is found using the Central Limit Theorem, which states that the sampling distribution of the sample mean will be normally distributed if the sample size is large enough (n ≥ 30 in this case, so the condition is met). The standard error of the mean (SEM) is calculated as the population standard deviation divided by the square root of the sample size, which is 4 / sqrt(64) = 4 / 8 = 0.5. To find the probability that the sample mean is less than 14 minutes, we calculate the Z-score: (14 - 15) / 0.5 = -2. The Z-score of -2 corresponds to a probability of 0.0228, indicating the likelihood that a sample mean is less than 14 minutes given the population parameters.

Albert Abbasi, VP of Operations at Ingleside International Bank, Is