Exam P Practice Problem 101 – auto collision claims
Problem 101A
The amount paid on an auto collision claim by an insurance company follows a distribution with the following density function.
The insurance company paid 64 claims in a certain month. Determine the approximate probability that the average amount paid is between 7.36 and 8.84.
Problem 101B
The amount paid on an auto collision claim by an insurance company follows a distribution with the following density function.
The insurance company paid 36 claims in a certain month. Determine the approximate 25th percentile for the average claims paid in that month.
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Exam P Practice Problem 83 – Claim Size of Auto Insurance Policies
Problem 83A
An insurance company has a block of auto insurance policies. The claim size (in thousands) for a policy in this block of auto insurance policies is modeled by the random variable where has a normal distribution with mean 0 and variance 1.5.
What is the expected claim size for such an auto insurance policy?
Problem 83B
An insurance company has a block of auto insurance policies. The claim size (in thousands) for a policy in this block of auto insurance policies is modeled by the random variable where has a normal distribution with mean 0 and variance 3.
What is the standard deviation of the claim size for such an auto insurance policy?
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Answers

Answers can be found in this page.
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Exam P Practice Problem 66 – Median Cholesterol Level
Problem 66A
The blood cholesterol levels of men aged 55 to 64 are normally distributed with mean 225 milligrams per deciliter (mg/dL) and standard deviation 39.5 mg/dL.
A medical researcher is planning a clinical study targeting men from the age group of 55 to 64 who have high blood cholesterol levels (above 240 mg/dL).
What is the median cholesterol level of the men in the target population of this medical study?
Problem 66B
The blood cholesterol levels of women aged 55 to 64 are normally distributed with mean 190 milligrams per deciliter (mg/dL) and standard deviation 40 mg/dL.
A medical researcher is planning a clinical study targeting women from the age group of 55 to 64 who have borderline high blood cholesterol levels (between 200 and 240 mg/dL).
What is the median cholesterol level of the women in the target population of this medical study?
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Answers
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Exam P Practice Problem 58 – Dental Care and Vision Care Expenses
Problem 58A
A health plan offers dental care and vision care benefits. Let represents the total annual amount (in millions) paid in dental care benefits. Let represents the total annual amount (in millions) paid in vision care benefits.
The health plan determined that
 where follows a normal distribution with mean 0 and variance 1,
 where follows a normal distribution with mean 0 and variance 2, and
 and are independent.
Given that the total annual vision care benefits paid by the health plan exceeds 2.5 millions, what is the probability that the total annual dental care benefits paid by the health plan exceeds 2 millions?
Problem 58B
A health plan offers dental care and vision care benefits. Let represents the total annual amount (in millions) paid in dental care benefits. Let represents the total annual amount (in millions) paid in vision care benefits.
The health plan determined that
 where follows a normal distribution with mean 0 and variance 1,
 where follows a normal distribution with mean 0 and variance 1, and
 and are independent.
What is the probability that the total annual dental care benefits exceeds 3 millions and that the total annual vision care benefits exceeds 4 millions?
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Answers

Answers can be found in this page.
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Exam P Practice Problem 52 – Reliability of Refrigerators
Problem 52A
The time from initial purchase to the time of the first major repair (in years) for a brand of refrigerators is modeled by the random variable where is normally distributed with mean 1.2 and variance 2.25.
A customer just bought a brand new refrigerator of this particular brand. The refrigerator came with a twoyear warranty. During the warranty period, any repairs, both minor and major, are the responsibilities of the manufacturer.
What is the probability that the newly purchased refrigerator will not require major repairs during the warranty period?
Problem 52B
The time from initial purchase to the time of the first major repair (in years) for a brand of refrigerators is modeled by the random variable where is normally distributed with mean 0.8 and standard deviation 1.5.
What is the median length of time (from initial purchase) that is free of any need for major repairs?
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Answers

Answers can be found in this page.
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Exam P Practice Problem 45 – Heights of Male Students
Problem 45A
Heights of male students in a large university follow a normal distribution with mean 69 inches and standard deviation 2.8 inches.
Five male students from this university are randomly selected.
What is the probability that the shortest student among the five randomly selected students is taller than 5 feet 5 inches?
Note that one feet = 12 inches.
The answers are based on this normal table from SOA.
Problem 45B
Heights of male students in a large university follow a normal distribution with mean 69 inches and standard deviation 2.8 inches.
Ten male students from this university are randomly selected.
What is the probability that the tallest student among the ten randomly selected students is shorter than 6 feet 2 inches?
Note that one feet = 12 inches.
The answers are based on this normal table from SOA.
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Answers
The answers are based on this normal table from SOA.
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