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 55 and a standard deviation of 4. using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 51 and 59? do not enter the percent symbol. ans = %

Explanation:

Step1: Identify the mean and standard - deviation

The mean $\mu = 55$ and the standard deviation $\sigma=4$.

Step2: Calculate the z - scores

For $x = 51$, the z - score $z_1=\frac{51 - 55}{4}=\frac{- 4}{4}=-1$.
For $x = 59$, the z - score $z_2=\frac{59 - 55}{4}=\frac{4}{4}=1$.

Step3: Apply the empirical rule

The empirical rule states that for a bell - shaped distribution, approximately 68% of the data lies within 1 standard deviation of the mean. That is, the percentage of data between $z=-1$ and $z = 1$ is 68.

Answer:

68