SOLUTION: (Please help me with this question?) Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $120,

Question 862717: (Please help me with this question?)
Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $120,000. This distribution follows the normal distribution with a standard deviation of $38,000.
(a)
If we select a random sample of 58 households, what is the standard error of the mean? (Round your answer to the nearest whole number.)
Standard error of the mean=?
(b) What is the expected shape of the distribution of the sample mean?

Not normal, the standard deviation is unknown.
Unknown.
Uniform
Normal.

(c)
What is the likelihood of selecting a sample with a mean of at least $124,000? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Probability=?
(d)
What is the likelihood of selecting a sample with a mean of more than $112,000? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Probability=?
(e)
Find the likelihood of selecting a sample with a mean of more than $112,000 but less than $124,000. (Round z value to 2 decimal places and final answer to 4 decimal places.)
Probability=?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
a) standard error of the mean = 38000 / square root(56) = 5078
b) normal
c) P(x > or = 124000) = 1 - P(x<124000)
we calculate the z score for P(x<124000)
124000 - 120000 / 5078 = 0.78771169751870815282 = 0.79
consult z table for probability assocated with z score = .79
P(x > or = 124000) = 1 - .79 = 0.21
d) P(x > or = 112000) = 1 - P(x<112000)
we calculate the z score for P(x<112000)
112000 - 120000 / 5078 = -1.58
consult -z table for probability assocated with z score = -1.58
P(x > 112000) = 1 - P(x<112000) = 1 - 0.06 = 0.94
e) P(x > 112000 and x < 124000) = P(x<124000) - P(x<112000) = 0.79 - 0.06 = 0.73

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

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

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

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

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

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

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