Using the empirical rule, what is the approximate percentage of daily phone calls numbering between 33 and 81?

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 57 and a standard deviation of 8. Using the empirical rule, what is the approximate percentage of daily phone calls numbering between 33 and 81?

Answer 1

33 is 24 less than 57, and 81 is 24 greater than 57. We know that the standard deviation is 8. Therefore, the total area of the bell curve we are encompassing is 3 standard deviations above and below 57, our mean. Thus, based on the empirical rule, we can easily conclude that the approximate percentage of daily phone calls numbering between 33 and 81 would be:

99.7%