Concept explainers
Whether the company can safely base its rates on the assumption that its average loss will be no greater than $275 or not if it sells 10,000 policies.
Answer to Problem 63E
The company can safely base its rates on the assumption that its average loss will be no greater than $275 it sells 10,000 policies.
Explanation of Solution
Given information:
The mean annual loss,
The standard deviation of the loss,
Formula used:
The central limit theorem states that if the
The z-value of a distribution can be found by dividing the difference between population mean and sample mean by the standard deviation that is,
Since, the sample size of 10,000 policies is at least 30; so we can apply the central limit theorem.
Find the z-value by using the formula
Substitute 275 for x, 250 for
Thus, the corresponding probability is:
Therefore, the company can safely assume that the average loss will be no greater than $275 because the probability is almost zero.
Hence, the company can safely base its rates on the assumption that its average loss will be no greater than $275 it sells 10,000 policies.
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