All the sales representatives at Allcity Insurance are female, and their mean annual salary is $60,000 with a standard deviation of $5,000. All customer account managers are male and they have a mean salary of $80,000 with a standard deviation of $15,000. Heather knows she is one standard deviation above the mean of the sales representatives. She wants to transfer to become the first female customer account manager and will begin at her same salary. After she transfers, compared to the customer account managers her salary will be at what z-score?
A) -2
B) -1
C) 0
D) +1

Question

Quizplus · Accepted Answer

Heather's salary as a sales representative is one standard deviation above the mean for her group, so her salary is $60,000 + $5,000 = $65,000. To find her z-score among the customer account managers, we use the formula $z = \frac{(X - \mu)}{\sigma}$, where $X$ is Heather's salary, $\mu$ is the mean salary of the customer account managers, and $\sigma$ is the standard deviation of the customer account managers' salaries. Plugging in the values, we get $z = \frac{(65,000 - 80,000)}{15,000} = \frac{-15,000}{15,000} = -1$. This means Heather's salary will be 1 standard deviation below the mean salary of the customer account managers.

All the Sales Representatives at Allcity Insurance Are Female, and Their