Question

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 40 minutes and a standard deviation of 16 minutes, the probability that Albert's sample of 100 will have a mean between 38.4 and 41.6 minutes is ________

0.75

0.55

0.68

0.87

0.98

Answer 1

Given that, mean (μ) = 40 minutes and

standard deviation = 16 minutes

sample size (n) = 100

We want to find,

z-score for is,

z-score for is,

That is to find, P(-1 < Z < 1)

According to Empirical rule, approximately 68% of the data fall within 1 standard deviations of the mean.

Therefore, the probability that Albert's sample of 100 will have a mean between 38.4 and 41.6 minutes is 0.68.

Answer : 0.68