# The weekly incomes of a large group of middle managers are normally distributed

August 30, 2017

Question
The weekly incomes of a large group of middle managers are normally distributed with a mean of \$1,500 and a standard deviation of \$150. Use the normal distribution to calculate thefollowing:

1. Find the probability that a particular weeklyincome selected at random is between \$750 and \$1,500?

2. What is the probability that the income is lessthan \$900?

3. What is the probability that the income is morethan \$1100?

4. What is the probability that the income isbetween \$1,000 and \$1,800? (Be able to draw a graph to illustrate your results.)

5. Find the salary that represents the 50thpercentile.

6. Find the salary that represents the 90thpercentile.

7. 5% of the salaries are below what value?

8. The top 5% of the salaries are above what value?

9. Between which two values will the middle 50% ofthe data lie?

10. Whatpercent of the managers make more than \$1200 a month?

11. Use theempirical rule to determine the following:

A About 68%of the observations lie between which two values?

B About 95%of the observations lie between which two values?

C About 99%of the observations lie between which two values?

12. Use thenormal distribution to determine the following:

A 68% of theobservations lie between which two values?

B 95% ofthe observations lie between which two values?

C 99% of the observations lie between which twovalues?

13. Discussthe differences in the results for question 12 and question 1

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