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 3. Using the
empirical rule, what is the approximate percentage of daily phone calls numbering between 57 and
63?

Answer 1

Prob ( 41 <= X <= 77) =

Prob ( (41-59)/9 <= Z <= (77-59)/9 ) = <--- changes to z scores

Prob ( -18/9 <= Z <= 18/9 ) =

Prob ( -2 <= Z <= 2) =

Prob ( z<=2) - Prob(Z<=-2) = <--- by property of the normal bell curve

= 0.9772 - 0.0228 <--- per the normal distribution table

= 0.9544

Explanation:

make sense ?