Question

in a mid - size company, the distribution of the number of phone calls answered each day by the receptionists is approximately normal and has a mean of 63 and a standard deviation of 4. using the 68 - 95 - 99.7 rule (empirical rule), what is the approximate percentage of daily phone calls numbering between 59 and 67?

Explanation:

Step1: Find the number of standard deviations from the mean

The mean $\mu = 63$ and the standard deviation $\sigma=4$.
For $x_1 = 59$, $z_1=\frac{59 - 63}{4}=\frac{- 4}{4}=-1$
For $x_2 = 67$, $z_2=\frac{67 - 63}{4}=\frac{4}{4}=1$

Step2: Apply the 68 - 95 - 99.7 rule

The 68 - 95 - 99.7 rule (Empirical Rule) states that for a normal distribution, approximately $P(\mu-\sigmaSince $59=\mu-\sigma$ and $67=\mu+\sigma$, the percentage of data between $59$ and $67$ is $68\%$

Answer:

$68$