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 48 and a standard deviation of 3. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 39 and 57?

Answer 1

Given:

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.

The mean = μ = 48

The standard deviation = σ = 3

We will find the percentage of daily phone calls numbering between 39 and 57

We will use the following formula:

`z=(x-\mu)/(\sigma)`

We will find the value of z when x = 39 and x = 57

`\begin{gathered} x=39\to z=(39-48)/(3)=-3 \\ \\ x=57\to z=(57-48)/(3)=(9)/(3)=-3 \end{gathered}`

We will use the tables of the z-scores to find P( -3 < z < 3)

[tex]P(-3So, the answer will be, that the percentage = 99.73%