Question

An insurance company sells a policy to airline passengers. If a flier misses the purchased flight due to medical reasons, the policy gives $300 to the flier. Otherwise, there is no return. Records show that about 5% passengers miss flight due to illness. You buy the policy for your next flight. Select the correct statement.

(A) The expected value of the amount of money you receive is $15. (B) The variance of the amount of money you receive is $4275. (C) The amount of money you could receive is either $0 or $300. (D) All of the above are correct.

Answer 1

X: The amount of money you receive (from the policy)

The possible value of X

X=0 if you do not miss the flight or you miss for reasons other than illness;

X= $300 if you miss the flight due to illness.

Given , Records show that about 5% passengers miss flight due to illness

Therefore, Probability that you miss flight due to illness = 5/100 = 0.05

Probability that you don't miss the flight or you miss for reasons other than illness = 1-0.05 =0.95

Therefore P(X=300) = 0.05 ; P(X=0) = 0.95

X: The amount of money you receive

Expected value of X

The expected value of the amount of money you receive is $15

Var(X) = E(X²) -E(X)²

Var(X) = E(X²) -E(X)² = 4500 - 15² = 4500 - 225 = 4275

The variance of the amount of money you receive is $4275

The possible value of X are 0 or 300

The amount of money you could receive is either $0 or $300

The expected value of the amount of money you receive is $15 - correct

The variance of the amount of money you receive is $4275 - Correct

The amount of money you could receive is either $0 or $300 - Correct

Ans : (D) All of the above are correct.