Question:

a) Let X be a normally distributed random variable with parameters m and s. Find the value of k such that:

P(m - ks £ X £ m + ks) = 0.3034.

b) The Oregon Insurance Company sells insurance policies to protect the wood siding on your home against damage by Spotted Owls. It sells this policy on a $100,000 home for a $2000 per year premium. (This annual payment is made to the company at the beginning of every year.)

Based on historical records, the company estimates these probabilities:

(i) 0.01 that the house will be attacked by Spotted Owls in any given year and be a complete loss of $100,000.

(ii) 0.02 that the house will sustain partial damage by Spotted Owls in any given year and suffer $40,000 damage.

(iii) 0.97 that the house will not sustain any Spotted Owl damage in any given year.

(This implies that there is 0 probability that the house will suffer Spotted Owl damage more than once in any year.)

Find the Insurance Company's expected profit per year for a single policy.