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 43 and a standard deviation of 7. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 22 and 64?

answer= %?

Answer 1

Solution:

The given standard deviation is 7,and the mean is 38.

Formula is, z = (X-Mean) / S.D

z value corresponding to X = 22 is

z = (22-43)/7

= -21/7

= -3

z value corresponding to X = 64

z = (64-43)/7

= 21/7

= 3

According to the empirical rule "The empirical rule" is also called as the three-sigma rule (i.e 68-95-99.7 rule), We have to know one standard deviation of the mean,covers 68% of data, two standard deviation of the mean,covers 95% of data, three standard deviation of the mean,covers 99.7% of data, Therefore +/- to the 3rd three standard deviation covers of the items 99.7% of data. Therefore the percentage of daily phone calls numbering between 22 and 64 = 99.7%

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