Online Exam: College

Actuaries in the U.S., Canada and other parts of the world earn professional credentials by passing a series of examinations. This Online Exam is designed to give you an idea of the types of questions you might encounter on the preliminary actuarial examinations administered by the Casualty Actuarial Society and Society of Actuaries. Please be sure to review the Actuarial Exams section of the Web Site, where you can access complete sample actuarial exams.

Answer the five multiple choice questions below, then click submit to see your results. If you are a high school student, please take our High School version of the Online Exam.

1.

In calendar year 2003, the medical claim costs per employee of a company is estimated to have the following probability density function:

f(x) = k × e^{- x / 2}                                        x > 0

where k is a constant that you need to calculate, and x is in units of $1000.

What is the probability that costs per employee in 2003 will exceed $6000.

2.

A medical researcher conducts a ten-week study of patients infected with a chronic disease. Over the course of the study, the researcher finds that the fraction of patients exhibiting severe symptoms can be modeled as

where t is time elapsed, in weeks, since the study began.

What is the minimum fraction of patients exhibiting severe symptoms between the end of the first week and the end of the seventh week of the study?

3.

The number of items produced by a manufacturer is given by p = 100 , where x is the amount of capital and y is the amount of labor. At a particular point in time:

(i)     the manufacturer has 2 units of capital,
(ii)     capital is increasing at a rate of 1 unit per month,
(iii)     the manufacturer has 3 units of labor, and
(iv)     labor is decreasing at a rate of 0.5 units per month.

Determine the rate of change in the number of items produced at the given time.

4.

Ten percent of an insurance company's policyholders had at least one claim in the past five years. The rest had none.

For each policyholder who had at least one claim in the past five years, the probability of having a claim this year is 0.15. For the rest, the probability of having a claim is 0.05.

Given that a policyholder has a claim this year, what is the probability that this policyholder had at least one claim in the past five years.

5.

What is the average age to which a 90-year old man will live, given that the probability a person age x will die before age x+1 is (x - 89) / 5?