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 46 and a standard deviation of 3. Using the empirical rule, what is the approximate percentage of daily phone calls numbering between 43 and 49

Answer 1

P( 43 ≤ X ≤ 49) = 0.9545

Explanation:

We are given mean of 46 and a standard deviation of 3

We want to find the percentage of daily phone calls numbering between 43 and 49. This can be written as;

P( 43 ≤ X ≤ 49)

Using the z-formula, we have;

z = (x - μ)/s

This transforms to;

P((43 - 46)/3)) ≤ Z ≤ ((49 - 46)/3))

This gives;

P(-2) ≤ Z ≤ P(2)

From z - table attached, P(-2) = 0.02275 and P(2) = 0.97725

Thus;

P( 43 ≤ X ≤ 49) = 0.97725 - 0.02275

P( 43 ≤ X ≤ 49) = 0.9545