SOLUTION: Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $110,000. This distribution follows the norma

Question 240859: Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $110,000. This distribution follows the normal distribution with a standard deviation of $40,000.
a. If we select a random sample of 50 households, what is the standard error of the mean?
b. What is the expected shape of the distribution of the sample mean?
c. What is the likelihood of selecting a sample with a mean of at least $112,000?
d. What is the likelihood of selecting a sample with a mean of more than $100,000
e. What is the likelihood of selecting a sample with a mean of more than $100,000 but less than $112,000?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $110,000. This distribution follows the normal distribution with a standard deviation of $40,000.
a. If we select a random sample of 50 households, what is the standard error of the mean?
The standard error depends on the level of significance.
If alpha is 5%, SE = 2.0096*40,000/sqrt(50) = 11369.0143
-------------------------------------------------------------
b. What is the expected shape of the distribution of the sample mean?
Normal with mean = 110,000 and std = 40,000/sqrt(25) = 5656.85
--------------------------------------------------------------
c. What is the likelihood of selecting a sample with a mean of at least $112,000?
t(112,000)= (112,000-110,000)/[40,000/sqrt(50)] = 0.3536..
-----------------
P(x >= 112000) = P(t >= 0.3536 with df = 49) = 0.3626
================================================================
d. What is the likelihood of selecting a sample with a mean of more than $100,000
Same process as "c"
----------------------------
e. What is the likelihood of selecting a sample with a mean of more than $100,000 but less than $112,000?
Combine the t-values from "c" and "d".
===========================================
Cheers,
Stan H.

RELATED QUESTIONS
Information from the American Institute of Insurance indicates the mean amount of life... (answered by Boreal)

Information from the American Institute of Insurance indicates the mean amount of the... (answered by stanbon)

This is from the textbook Statistical Techniques in Business and Economics, 13th edition, (answered by stanbon)

i really need some help with this problem, I am really struggling with it.... (answered by stanbon)

32. Information from the American Institute of Insurance indicates the mean amount of... (answered by edjones)

Information from the American Institute of Insurance indicates the mean amount of life... (answered by Boreal)

**Please help*** 8-10 Information from the American Institute of Insurance indicates... (answered by Theo)

(I'm stuck on this problem. Can someone please help?) Information from the American... (answered by jim_thompson5910)

(Please help me with this question?) Information from the American Institute of... (answered by rothauserc)