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version 2 Questions 11 13 Suppose that when you buy a smartphone, you can also buy a protection plan at $21. The protection plan will compensate $100 to you if your smartphone is broken. The insurance company makes profit when the premium of the plan exceeds the average claim per plan. Assume that the probability of a smartphone being broken is 20% and that the event is statistically independent across smartphones. The following table may help when you calculate the standard deviation. 11 121 14 196 17 289 15 225 18 324 12 144 16 256 19 361 13 169 Q11 What is the expected profit per plan? (a) $ (b) $100 (e) $19 (d) $20 (e) $81 Answer (a) $1 Q12 If 100 smartphones are insured by the protection plan, what is the probability that the insurance company makes profit? (a) 69.146% (b) 93.319 % (c) 59.871% (d) 99.379% (e) 81.359% Answer (e) Q13 If 400 smartphones are insured by the protection plan, what is the probability that the protection plan makes profit? (a) 69.146% (b) 93.319% (e) 59.871 % (d) 99.379% (e) 81.359% Answer (a) 6

Answer 1

Profit profit if no compensation = 21 if compensation = 21-100 =8-19 - 2 C) Expected pagit = 20 + (-74) + 80 (21) 2017 + (20)

Ans a $1 1 ) E (P2) = 20 (-70)² + 30 (21)2 = 1248.2 + 352.8. Variance - Var (P = E(P²) - (66f)) = 1601 -

DI Pg. Standard deviation = 1600 = 40 z statistic o - 1 - 1x10 - 0.25 . It will pllow normal distribution as nslod o bolo is taken because we want the case where to company makes phoit so above o is profit only

makes pugit , so above o is profit only Sering Dalue Probability of company making profit : 0.5817 P ( 2 z 3-0.25) = D B table This is translato to 59.87% Ans )

Bo Following same process as lost question 2 statistic = = cat) (20)

2 statistic = Probability company manas profit P ( 2 ² -0.5 = 0.6915 This becomes 69.15)