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gladu [14]
3 years ago
15

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.
Mathematics
1 answer:
zlopas [31]3 years ago
7 0

Answer:

Salary: $90,500

Step-by-step explanation:

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

Z = \frac{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 = \frac{X - \mu}{\sigma}

1.24 = \frac{X - 80000}{8450}

X - 80000 = 1.24*8450

X = 90478

Rouded to the nearest hundred of dollars:

Salary: $90,500

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