Question

22. A management consulting firm is evaluating the salary structure for a large insurance company The goal of the study is to develop salary ranges for each of the possible job grades within the company. The company and the firm have agreed that a reasonable salary range for each job grade can be determined by finding the salary range in which 95% of the current salaries for that job grade fall. The average salary and the standard deviation of the salaries are listed in the following table for three of the job grades. Table for Exercise 22 - Salaries ($) Job Grade 25 22,000 1500 40 45,000 5000 35,000 2000 a. Determine the appropriate salary ranges for the three job grades. b. What assumption did you make about the salaries in each of the job grades in answering part a.?

Answer 1

a. According to empirical rule, 95% of the data lie within two standard deviations .

For job grade 25 :

( $\overline{x}-2*s,\overline{x}+2s$ )

( 22000 - 2 * 1500, 22000+2*1500 )

( 19000, 25000 )

For job grade 33 :

( $\overline{x}-2*s,\overline{x}+2s$ )

( 35000 - 2 * 2000, 35000+2*2000 )

( 31000, 39000 )

For job grade 40 :

( $\overline{x}-2*s,\overline{x}+2s$ )

( 45000 - 2 * 5000, 45000+2*5000 )

( 35000, 55000 )

b. Assumptions :

1. Sample is randomly drawn from normally distributed population.

2. Sample size is considered to be large enough.

3. Samples are independents.