The z-score of the score, 58, for the number of calls can be calculated using the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
where μ is the mean and σ is the standard deviation.
From the question, we have the following parameters:
[tex]\begin{gathered} \mu=34 \\ \sigma=12 \end{gathered}[/tex]
Therefore, the z-score is calculated to be:
[tex]\begin{gathered} z=\frac{58-34}{12} \\ z=\frac{24}{12} \\ z=2 \end{gathered}[/tex]
Using a probability calculator, the probability for the z-score is given to be:
[tex]P(z>2)=0.02275[/tex]
Given the probability value, we can calculate the expected value of this event for the survey size of 100 to be:
[tex]EV=0.02275\times100=2.275[/tex]
Therefore, approximately 2 installers made more than 58 service calls.
