Information from the AmericanInstitute of Insurance indicates the mean amount of
ID: 2954983 • Letter: I
Question
Information from the AmericanInstitute of Insurance indicates the mean amount oflife
insurance per household in theUnited States is $110,000. This distribution followsthe
normal distribution with astandard deviation of $40,000.
a.If we select a random sampleof 50 households, what is the standard error of themean?
b.What is the expected shape ofthe distribution of the samplemean?
c.What is the likelihood ofselecting a sample with a mean of at least$112,000?
d.What is the likelihood ofselecting a sample with a mean of more than$100,000?
e.Find the likelihood ofselecting a sample with a mean of more than $100,000 butless
than$112,000.
Explanation / Answer
Given =110000, =40000
(a) The standard error of the mean is
/n
= 40000/sqrt(50)
=5656.854