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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
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Annual incomes for heads of household in a section of a

Chapter 4, Problem 108E

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QUESTION:

Problem 108E

Annual incomes for heads of household in a section of a city have approximately a gamma distribution with α = 20 and β = 1000.

a Find the mean and variance of these incomes.

b Would you expect to find many incomes in excess of $30,000 in this section of the city?

c Applet Exercise What proportion of heads of households in this section of the city have incomes in excess of $30,000?

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QUESTION:

Problem 108E

Annual incomes for heads of household in a section of a city have approximately a gamma distribution with α = 20 and β = 1000.

a Find the mean and variance of these incomes.

b Would you expect to find many incomes in excess of $30,000 in this section of the city?

c Applet Exercise What proportion of heads of households in this section of the city have incomes in excess of $30,000?

ANSWER:

Solution:

Step 1 of 3:

The annual incomes for heads of household in a section of a city have approximately a gamma distribution with and .

We have find,

  1. The mean and variance of these incomes,
  2. How many incomes we can find in this section of the city that more than $30,000,
  3. The proportion of heads of households in this section of the city have in excess of $30000.

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