ISMT111 Problem Set #6
(1)
A psychologist has designed a new aptitute test for life insurance companies to use to screen
applicants for beginning actuarial positions. To estimate the mean score achieved by all future
applicants who will eventually take the test, the psychologist has administered the test to nine
randomly selected persons. The sample mean and standard deviation have been calculated
to be 83.7 points and 12.9 points respectively. By assuming that the test scores of all future
applicants are approximately normally distributed, the psychologist reported that a conﬁdence
interval estimate for the mean score to be 71.247 to 96.153. What level of conﬁdence the
psychologist has used in constructing this estimate?
(2)
An investment ﬁrm in Los Angeles is interested in determining the mean annual rate of return
for all common stocks sold on the New York Stock Exchange. A random sample of 100 such
stocks is selected and for this sample the following information is determined:
mean rate of return is 10.57%;
standard deviation of rate of return is 12.10%.
Construct a 95% conﬁdence interval estimate of the mean annual rate of return of all such
stocks.
(3)
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 Fall '09
 AnthonyChan
 Normal Distribution, Standard Deviation, confidence interval estimate, 3M Company

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