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.

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.

	A. 41
	B. 61
	C. 82
	D. 102
	E. 245

The claim amount on a certain insurance contract has a normal distribution with mean $3,300 and standard deviation $575. Given 25 independent claims, what is the probability that the number of claims less than $2700 is less than or equal to 4?

	A. 0.26
	B. 0.45
	C. 0.5
	D. 0.69
	E. 0.82

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?

	A. 91
	B. 91.5
	C. 92
	D. 92.5
	E. 93

An insurance company issues policies to two groups of insured A and B. For a certain type of coverage, the number of claims per year for each group follows the Poisson distribution

For group A, = 1, and for group B, = 1.5.

If in calendar year 2003, 2/5 of this company's policyholders are of group A, what is the probability that the combined number of claims from both groups is no more that two.

	A. 0.627
	B. 0.857
	C. 0.544
	D. 0.287
	E. 0.879

The joint probability density function of the loss amount X, and the expenses associated with that loss Y, is given by

f(x,y) = 4 e ^-2(x+y) for x>0, y>0.

Assuming an insurance policy is written to reimburse the total amount of loss plus expense X+Y, calculate the probability that the reimbursement would be less than 1.

	A. 1 + e^-2
	B. 1 - 2 e^{- 2}
	C. 1 - 3 e^{- 2}
	D. 2 - 4 e^{- 2}
	E. 1 + 3 e^{- 2}