Question

Salaries for an large engineering company are normally distributed with a mean of $80,000 and a standard deviation of $8,450. An employee was having their annual appraisal and the manager indicated that the employee salary for next year has a Z-score of 1.24. Approximately how much will this employee be paid next year in salary? Salary=$[salary] Enter your answer to the nearest hundred of dollars, i.e 50,185 would be entered 50,200.

Answer 1

Salary: $90,500

Explanation:

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

`\mu = 80000, \sigma = 8450`

An employee was having their annual appraisal and the manager indicated that the employee salary for next year has a Z-score of 1.24. Approximately how much will this employee be paid next year in salary?

This is X when
`Z = 1.24`. So

`Z = (X - \mu)/(\sigma)`

`1.24 = (X - 80000)/(8450)`

`X - 80000 = 1.24*8450`

`X = 90478`

Rouded to the nearest hundred of dollars:

Salary: $90,500