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:
[tex]z=\frac{x-\mu}{\sigma}[/tex]We will find the value of z when x = 39 and x = 57
[tex]\begin{gathered} x=39\to z=\frac{39-48}{3}=-3 \\ \\ x=57\to z=\frac{57-48}{3}=\frac{9}{3}=-3 \end{gathered}[/tex]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%