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.

Salary: $90,500

Step-by-step explanation:

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

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:

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 . So

Rouded to the nearest hundred of dollars:

Salary: $90,500