At a costumer service call center for a large company, the number of calls received per hour is normally distributed with a mean of 150 calls and a standard deviation of 5 calls. What is the probability that during a given hour of the day there will be between 146 calls and 163 calls, to the nearest thousandth

We have been given that at a customer service call center for a large company, the number of calls received per hour is normally distributed with a mean of 150 calls and a standard deviation of 5 calls. We are asked to find the probability that during a given hour of the day there will be between 146 calls and 163 calls.

First of all, we will use z-score formula to find z-score corresponding to 146 and 163.

Our next step is to find percentage of data scores falls between both z-scores.

Using normal distribution table, we will get:

Let us convert our answer into percentage.

Upon rounding our answer to nearest thousandths, we will get:

Therefore, the probability that during a given hour of the day there will be between 146 calls and 163 calls is approximately .

correct answers below: