Question

Refer to the picture:I just need help with answering letter D.

Answer 1

The z-score of the score, 58, for the number of calls can be calculated using the formula:

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

where μ is the mean and σ is the standard deviation.

From the question, we have the following parameters:

`\begin{gathered} \mu=34 \\ \sigma=12 \end{gathered}`

Therefore, the z-score is calculated to be:

`\begin{gathered} z=(58-34)/(12) \\ z=(24)/(12) \\ z=2 \end{gathered}`

Using a probability calculator, the probability for the z-score is given to be:

`P(z>2)=0.02275`

Given the probability value, we can calculate the expected value of this event for the survey size of 100 to be:

`EV=0.02275*100=2.275`

Therefore, approximately 2 installers made more than 58 service calls.