Question

The long-distance calls made by South Africans are normally distributed with a mean of 16.3 minutes and a standard deviation of 4.2 minutes for 1500 south Africans what is the expected number of callers whose calls last less than 15 minutes?

Answer 1

The question provides the following parameters:

`\begin{gathered} \mu=16.3 \\ \sigma=4.2 \end{gathered}`

For 15 minutes, the z-score is calculated using the formula:

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

At x = 15:

`z=(15-16.3)/(4.2)=-0.3`

The probability is calculated using the formula:

The expected number of callers will be calculated using the formula:

`\begin{gathered} E=xP(x) \\ At\text{ }x=1500 \\ E=1500*0.38 \\ E=570 \end{gathered}`

Therefore, the expected number of callers whose calls last less than 15 minutes is 570 callers.