The Mountain States Office of State Farm Insurance Company reports that approximately 84% of all automobile damage liability claims were made by people under 25 years of age. A random sample of ten automobile insurance liability claims is under study.

The Mountain States Office of State Farm Insurance Company reports that approximately 84% of all automobile damage liability claims were made by people under 25 years of age. A random sample of twelve automobile insurance liability claims is under study.

Find the mean and standard deviation of this probability distribution.

For samples of size 12, what is the expected number of claims made by people under 25 years of age?

What is mean?

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.

Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.

Given that:-

The Mountain States Office of State Farm Insurance Company reports that approximately 84% of all automobile damage liability claims were made by people under 25 years of age.
We need to find For samples of size 12, what is the expected number of claims made by people under 25 years of age?

The mean will be calculated by the formula below:-

Mean = [tex]\mu[/tex] = np = 12 x 0.84 = 10.08

The standard deviation will be calculated as:-

Standard deviation = [tex]\sqrt{npq}[/tex] = [tex]\sqrt{12\times 0.84\times 0.16}[/tex] = 1.27

Therefore the mean will be 10.08 and the standard deviation will be 1.27.

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