Question

In a mid-size company in Philadelphia, 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 57 and a standard deviation of 7. Using the empirical (68-95-99.7) rule, what is the approximate percentage of daily phone calls numbering between 50 and 64

Answer 1

Approximately 68% of daily phone calls will be in this interval.

Explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 57

Standard deviation = 7

What is the approximate percentage of daily phone calls numbering between 50 and 64

50 = 57 - 7

So 50 is one standard deviation below the mean

64 = 57 + 7

So 64 is one standard deviation above the mean

By the Empirical Rule, approximately 68% of daily phone calls will be in this interval.