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

Algebra ->  Probability-and-statistics -> 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      Log On


   

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) About Me  (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.