According to Salary Wizard the average base salary for a bra

According to Salary Wizard, the average base salary for a brand manager in Houston, Texas, is $88,592 and the average base salary for a brand manager in Los Angeles, California, is $97,417 (Salary Wizard website, February 27, 2008). Assume that salaries are normally distributed, the standard deviation for brand managers in Houston is $19,900, and the standard deviation for brand managers in Los Angeles is $21,800.

A.What is the probability that a brand manager in Houston has a base salary in excess of $100,000 (to 4 decimals)?

B.What is the probability that a brand manager in Los Angeles has a base salary in excess of $100,000 (to 4 decimals)?

C.What is the probability that a brand manager in Los Angeles has a base salary of less than $75,000 (to 4 decimals)?

D.How much would a brand manager in Los Angeles have to make in order to have a higher salary than 99% of the brand managers in Houston? (to the nearest whole number)?

Solution

Houston: mean salary = $88592 stdev = $19900

LA: mean salary = $97417 stdev = $21800

a) Probability (Salary > 100000) Houston = 1 - P[Z = (100,000 - 88,592)/19900]

                                                = 1 - P[Z = 0.573]

                                                = 1 - 0.7167 = 0.2832

b) Probability (Salary > 100000) LA = 1 - P[Z = (100,000 - 97417)/21800]

                                                = 1 - P[Z = 0.1184]

                                                = 1 - 0.5471 = 0.4529

c) Probability (Salary < 75000) LA = P[Z = (75000 - 97417)/21800]

                                                = P[Z = -1.028]

                                                = 0.1519

d) p = 0.99 Z = 2.33

2.33 = (X - 88592)/19900

X = $134959

Brand manager will have to get $134959 to be more than 99% of managers in Houston have a salary