Problems 15 17 Insurance for an appliance costs 30 and will

Problems 15 - 17. Insurance for an appliance costs $30 and will pay $330 if the insured item breaks within 2 years. The insurance company estimates that 6% of the insured items will break within 2 years. Let X be the random variable that assigns to each outcome (item breaks, item does not break) the profit to the company. A negative value of X is a loss. Then the distribution of X is given by the following table. 15. Calculate the mean value of X. A) 6.9 B) 10.2 C) 13.5 D) 16.8 E) 20.1 16. Calculate the standard deviation of X. A) 56.2938 B) 64.6665 C) 71.9218 D) 78.3707 E) 84.1985 17. Suppose that the mean value of X for some insurance company turns out to be $5 and the standard deviation turns out to be $55. The company sells 121 contracts. Find the probability that the company looses money.

Solution

Mean of X = 30(0.94) -300(0.06) = 28.2-18 = 10.2

Option B

E(X^2) = (900)(0.94)+300^2(0.06)

= 84.60+5400= 5484.6

Var(x) = 5484.6-104.04 =

Std dev = 73.35

Hence option C