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 60 and a standard deviation of 11. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 27 and 93?

Answer 1

Answer and Step-by-step explanation:

The empirical rule, also known as the 68-95-99.7 rule, states that for a bell-shaped or normal distribution:

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

- About 95% falls within two standard deviations.

- About 99.7% falls within three standard deviations.

Given that the mean is 60 and the standard deviation is 11:

1 standard deviation from the mean in this case would be between 60 - 11 = 49 and 60 + 11 = 71 calls.

Thus, within 1 standard deviation from the mean, approximately 68% of the phone calls fall.

Now, to find the percentage of phone calls between 27 and 93, we'll look at how many standard deviations away these values are from the mean:

For 27:

27-60/11 = -33/11 = - 3

For 93:

93-60/11 = 33/11 = 3

According to the empirical rule, within 3 standard deviations from the mean, about 99.7% of the data falls. This includes the range from \(27\) to \(93\). Therefore, the approximate percentage of daily phone calls numbering between 27 and 93 is approximately 99.7%.