Question

In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 36 and a standard deviation of 3. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 33 and 39? Do not enter the percent symbol. ans = %

Answer 1

According to the empirical rule (also known as the 68-95-99.7 rule), for a bell-shaped distribution, approximately:

- 68% of the data falls within one standard deviation of the mean.

- 95% falls within two standard deviations of the mean.

- 99.7% falls within three standard deviations of the mean.

In this case, the mean number of phone calls answered by each receptionist is 36, and the standard deviation is 3.

To calculate the percentage of daily phone calls numbering between 33 and 39, we need to find the proportion of data within one standard deviation of the mean in either direction.

The range of interest (33 to 39) is within one standard deviation of the mean, so approximately 68% of the data will fall within this range.

Therefore, the approximate percentage of daily phone calls numbering between 33 and 39 is 68%.