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 between 13.5 and 16.5 minutes is ________.
A) 0.9974
B) 0.4987
C) 0.9772
D) 0.4772
E) 0.5000

Question

Quizplus · Accepted Answer

The correct answer is A.The probability that Albert's sample of 64 will have a mean between 13.5 and 16.5 minutes can be calculated using the central limit theorem. The central limit theorem states that the distribution of sample means will be approximately normal, regardless of the shape of the population distribution, if the sample size is large enough.In this case, the sample size is 64, which is large enough to apply the central limit theorem. The mean of the sample means will be equal to the mean of the population, which is 15 minutes. The standard deviation of the sample means will be equal to the standard deviation of the population divided by the square root of the sample size, which is 4 minutes divided by the square root of 64, which is 1 minute.Therefore, the probability that Albert's sample of 64 will have a mean between 13.5 and 16.5 minutes can be calculated using the standard normal distribution. The z-score for 13.5 minutes is (13.5 - 15) / 1 = -1.5. The z-score for 16.5 minutes is (16.5 - 15) / 1 = 1.5. The probability that a standard normal random variable will fall between -1.5 and 1.5 is 0.9974.

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