An insurance company knows that in the entire population of millions of homeowne

Question

An insurance company knows that in the entire population of millions of homeowners, the mean annual loss from fire is = $250 and the standard deviation of the loss is = $1000. This distribution of losses is strongly right skewed: many homeowners had $0 loss and a few had very large losses. We want to compute the probability that a randomly selected homeowner will have a loss greater than $275.

1) Can we use the standard Normal table to find the probability? Why or why not?

a. Yes, because we want to find the probability on the loss of a randomly selected homeowner and losses have an approximately Normal distribution.

b. Yes, because we want to find the probability on a sample mean which has a Normal distribution since the population of losses is approximately Normal.

c. Yes, because we want to find the probability on a sample mean from a large random sample which has an approximately Normal distribution according to the Central Limit Theorem

d. No, because we cannot compute the probability on a loss using the standard Normal table since the shape of the distribution of losses is not Normal.

2)Refer to the distribution of homeowners losses from fire described in question above. We need to know whether the company can safely base its rates on the assumption that its mean loss will be no greater than $275 if it sells 10,000 policies. Should we use the standard Normal table to find the probability that the mean of a sample of 10,000 policies does not exceed $275?

a. Yes, because we want to find the probability on the loss of a randomly selected homeowner and losses have an approximately Normal distribution.

b. Yes, because we want to find the probability on a sample mean which has a Normal distribution since the distribution of losses is approximately Norm

c. Yes, because we want to find the probability on a sample mean from a large random sample which has an approximately Normal distribution according to the Central Limit Theorem.

d. No, because we cannot compute the probability on a loss using the standard Normal table since the shape of the distribution of losses is not Normal.

Explanation / Answer

1.

d. No, because we cannot compute the probability on a loss using the standard Normal table since the shape of the distribution of losses is not Normal. [ANSWER, D]

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2.

c. Yes, because we want to find the probability on a sample mean from a large random sample which has an approximately Normal distribution according to the Central Limit Theorem. [ANSWER, C]

By the central limit theorem, the sampling distirbution of means will be approximately normal even though the original distribution is not normal.

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