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Chapter 4: Problem 2

Employees of Corporation A earn annual salaries described by a mean of \(\$ 90,000\) and a standard deviation of \(\$ 10,000\). (a) The majority of all salaries fall between what two values? (b) A small minority of all salaries are less than what value? (c) A small minority of all salaries are more than what value? (d) Answer parts (a), (b), and (c) for Corporation B's employees, who earn annual salaries described by a mean of \(\$ 90,000\) and a standard deviation of \(\$ 2,000\).

Short Answer

Expert verified
The majority of Corporation A's salaries fall between $80,000 and $100,000, with a small minority less than $60,000 or more than $120,000. For Corporation B, the majority of salaries fall between $88,000 and $92,000, with a small minority less than $84,000 or more than $96,000.

Step by step solution

01

Determine Majority Salaries for Corporation A

To find the majority of salaries for Corporation A, add and subtract the standard deviation from the mean. So, majority falls between \(90,000 - 10,000 = $80,000\) and \(90,000 + 10,000 = $100,000\).
02

Determine Minority Salaries for Corporation A

To find the small minority of salaries for Corporation A, subtract and add three times the standard deviation from the mean. So, small minority of salaries are less than \(90,000 - 3*10,000 = $60,000\) and more than \(90,000 + 3*10,000 = $120,000\).
03

Determine Majority Salaries for Corporation B

Repeat step 1 for Corporation B, where standard deviation is $2,000. So, majority of Corporation B's salaries fall between \(90,000 - 2,000 = $88,000\) and \(90,000 + 2,000 = $92,000\).
04

Determine Minority Salaries for Corporation B

Repeat step 2 for Corporation B. So, small minority of Corporation B's salaries are less than \(90,000 - 3*2,000 = $84,000\) and more than \(90,000 + 3*2,000 = $96,000\).

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Most popular questions from this chapter

(a) While in office, a former governor of California proposed that all state employees receive the same pay raise of \(\$ 70\) per month. What effect, if any, would this raise have had on the mean and the standard deviation for the distribution of monthly wages in existence before the proposed raise? Hint: Imagine the effect of adding \(\$ 70\) to the monthly wages of each state employee on the mean and on the standard deviation (or on a more easily visualized measure of variability, such as the range). (b) Other California officials suggested that all state employees receive a pay raise of 5 percent. What effect, if any, would this raise have had on the mean and the standard deviation for the distribution of monthly wages in existence before the proposed raise? Hint: Imagine the effect of multiplying the monthly wages of each state employee by 5 percent on the mean and on the standard deviation or on the range.

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