Albert Abbasi, VP of Operations at Ingleside International Bank, is evaluating the service level provided to walk-in customers.

Answer:

The likelihood that Albert's sample of 64 will have a mean waiting time between 13.5 and 16.5 minutes is 0.9973.

Step-by-step explanation:

Prior concepts

A normal distribution is characterized as a "probability distribution that is symmetric around the mean, indicating that data close to the mean are more frequent than those further away".

The Z-score refers to "a statistical measurement that reflects the relationship of a value to the mean of a group, measured in standard deviations".

Let X denote the random variable of interest, and we identify its distribution:

Also, let signify the sample mean, whose distribution is:

In this case,

Solution to the problem

We seek this probability

Applying the Z-score formula to the probability results in:

To determine these probabilities, we can refer to normal distribution tables, use Excel, or a calculator.

The likelihood that Albert's sample of 64 will have a mean waiting time between 13.5 and 16.5 minutes is 0.9973.