SCENARIO 8-3
To become an actuary, it is necessary to pass a series of 10 exams, including the most
important one, an exam in probability and statistics.An insurance company wants to
estimate the mean score on this exam for actuarial students who have enrolled in a special
study program.They take a sample of 8 actuarial students in this program and determine
that their scores are: 2, 5, 8, 8, 7, 6, 5, and 7.This sample will be used to calculate a 90%
confidence interval for the mean score for actuarial students in the special study program.
-True or False: Referring to Scenario 8-3, for the confidence interval to be valid, it is
necessary that test scores of students in the special study program on the actuarial exam be
normally distributed.

Question

Quizplus · Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is large enough (n > 30). In this case, the sample size is 8, which is less than 30. However, the Central Limit Theorem can still be applied because the population distribution is approximately normal.

SCENARIO 8-3 to Become an Actuary, It Is Necessary to Pass a Pass