Question

In: Statistics and Probability

An insurance company has 20, 000 policyholders. The amount claimed yearly by a policyholder has an...

An insurance company has 20, 000 policyholders. The amount claimed yearly by a policyholder has

an expected value of $150 and a standard deviation of $750. Use the central limit theorem (CLT) to

approximate the probability that the the total amount claimed in the coming year will be larger than

3.3 million dollars.

Expert Solution

Total policyholders = n = 20000

mean = $150 and

standard deviation = $750

Where, 1 million dollar = 1000000 dollars

3.3 million dollars = 3.3 × 1000000 = $3300000

We want to find, the

probability that the the total amount claimed in the coming year will be larger than 3.3 million dollars.

sample mean = 3300000 / 20000 = $165

That is to find,

Therefore, required probability is 0.0023

orchestra answered 2 years ago

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