SOLUTION: Suppose that the annual household income in a small Midwestern community is normally distributed with a mean of $55,000 and a standard deviation of $4,500. a. What is the probabil

Question 1171892: Suppose that the annual household income in a small Midwestern community is normally distributed with a mean of $55,000 and a standard deviation of $4,500.
a. What is the probability that a randomly selected household will have an income between $50,000 and $65,000? (2 Marks)
b. What is the probability that a randomly selected household will have an income of more than $70,000? (2 Marks)
c. What minimum income does a household need to earn to be in the top 5% of incomes?
(2 Marks)
d. What maximum income does a household need to earn to be in the bottom 40% of incomes? (2 Marks)

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the mean is 55000.
the standard deviation is 4500.
the following calculator should help you answer these questions.
http://davidmlane.com/hyperstat/z_table.html
the answers to your questions are shown below:

a. What is the probability that a randomly selected household will have an income between $50,000 and $65,000? (2 Marks)

probability is .8536

b. What is the probability that a randomly selected household will have an income of more than $70,000? (2 Marks)

probability is .0004

c. What minimum income does a household need to earn to be in the top 5% of incomes?(2 Marks)

minimum income is 62401.842

d. What maximum income does a household need to earn to be in the bottom 40% of incomes? (2 Marks)

maximum income is 53859.938

i verified with the ti-84 plus that these answers are correct.

if you need to know how to do these manually through the use of the normal distribution tables, all you have to do is ask.

i can do them that way as well.
it just takes a little longer.
maybe even a little longer than that.

RELATED QUESTIONS
File: Gambling. The accompanying table shows a portion of the number of cases of crime... (answered by ikleyn)

The Easy Credit Company reports the following table representing a breakdown of costumers (answered by ikleyn)

Suppose the amount of healing oil used annually by household in Ontario is normally... (answered by ikleyn)

Suppose the mean amount of life insurance purchased by Canadian households is normally... (answered by Boreal)

Suppose the amount of heating oil used annually by households in Ontario is normally... (answered by Theo)

For the city of Quahog, R.I., assume the the mean household income is normally... (answered by stanbon)

Suppose household incomes in Indiana Co have a mean of $48,000 and a standard deviation... (answered by stanbon)

The government would like to conduct a subsidy program for the lowest 5 percent of the... (answered by Theo)

Suppose you construct 1000 confidence intervals of the mean US household annual income.... (answered by math_helper)