Question

In: Statistics and Probability

You just received a grant to study the motivation effects of pay level on employee performance....

You just received a grant to study the motivation effects of pay level on employee performance. Suppose you examine job performance scores for 630 employees, where a high score indicates good work performance. The results of your study determine the average performance score is 86, with a standard deviation of 11 points. Assuming a normal distribution, determine the percent and number of employees who:

a. What is the job performance score at the 29th percentile (6 pts)?

b. What is the job performance score at the 86th percentile (6 pts)?

Solutions

Expert Solution

Given that,

mean = = 86

standard deviation = = 11

n = 630

= 86

= / n = 11/ 630 = 0.4383

a. The z-distribution of the 29% is,

P(Z < z) = 29%

= P(Z < z ) = 0.29

= P(Z < -0.553 ) = 0.29

z = -0.553

Using z-score formula

= z * +

= -0.553 * 0.4383 + 86

= 85.76

Answer :- 85.76

b. The z-distribution of the 86% is,

P(Z < z) = 86%

= P(Z < z ) = 0.86

= P(Z < 1.080 ) = 0.86

z = 1.080

Using z-score formula

= z * +

= 1.080 * 0.4383 + 86

= 86.47

Answer :- 86.47

orchestra answered 1 year ago

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