Prob-Stats-Teacher-Book.pdf

# Practice exercise 2 p 26 1 we found that the average

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Practice Exercise 2 (p. 26) 1. We found that the average claim for a home in Happy Shores on the beach in a given year is \$14,700. Compute the standard deviation for the claim amount in a given year. Results Cat 5 Cat 4 Cat 3 Cat 2 Cat 1 TS NONE Claim Amt 500 350 100 50 25 5 0 Probability 0.01 0.01 0.01 0.05 0.08 0.14 0.7 Amt - Mean 485.3 335.3 85.3 35.3 10.3 -9.7 -14.7 (Amt - Mean)^2 235516.09 112426.1 7276.09 1246.09 106.09 94.09 216.09 Prob*(Amt - Mean)^2 2355.1609 1124.261 72.7609 62.3045 8.4872 13.1726 151.263 3787.41 Variance 61.54193692 Standard Deviation For the houses in Neighborhood A, we would expect to pay out \$14,700 with a standard deviation of \$62,000. Policyholder Outcome Payout (x) Probability P(X = x) Death 10,000 1/1000 Disability 5,000 2/1000 Neither 0 997/1000

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Page 17 MODULE 3 Additional Exercises (p. 26) NEIGHBOORHOD B Expected Value 8.225 Home Value (\$ thousands) Cat 5 Cat 4 Cat 3 Cat 2 Cat 1 TS None Probability 0.01 0.01 0.01 0.05 0.08 0.14 0.7 Damage % 250 80% 50% 15% 10% 8% 5% 0% Claim Amount 200 125 37.5 25 20 12.5 0 (Claim - Mean) 191.78 116.78 29.275 16.775 11.775 4.275 -8.225 (Claim - Mean)^2 36778 13636 857.03 281.4 138.65 18.276 67.651 Prob*(Claim - Mean)^2 367.78 136.36 8.5703 14.07 11.092 2.5586 47.355 Variance 587.78688 Std. Dev 24.244316 NEIGHBORHOOD C Expected Value 11.515 Home Value (\$ thousands) Cat 5 Cat 4 Cat 3 Cat 2 Cat 1 TS None Probability 0.01 0.01 0.01 0.05 0.08 0.14 0.7 Damage % 350 80% 50% 15% 10% 8% 5% 0% Claim Amount 280 175 52.5 35 28 17.5 0 (Claim - Mean) 268.49 163.49 40.985 23.485 16.485 5.985 -11.52 (Claim - Mean)^2 72084 26727 1679.8 551.55 271.76 35.82 132.6 Prob*(Claim - Mean)^2 720.84 267.27 16.798 27.577 21.74 5.0148 92.817 Variance 1152.0623 Std. Dev 33.942043
Page 18 MODULE 3 NEIGHBORHOOD D Expected Value 6.58 Home Value (\$ thousands) Cat 5 Cat 4 Cat 3 Cat 2 Cat 1 TS None Probability 0.01 0.01 0.01 0.05 0.08 0.14 0.7 Damage % 200 80% 50% 15% 10% 8% 5% 0% Claim Amount 160 100 30 20 16 10 0 (Claim - Mean) 153.42 93.42 23.42 13.42 9.42 3.42 -6.58 (Claim - Mean)^2 23538 8727.3 548.5 180.1 88.736 11.696 43.296 Prob*(Claim - Mean)^2 235.38 87.273 5.485 9.0048 7.0989 1.6375 30.307 Variance 376.1836 Std. Dev 19.395453 NEIGHBORHOOD E Expected Value 8.28 Home Value (\$ thousands) Cat 5 Cat 4 Cat 3 Cat 2 Cat 1 TS None Probability 0.01 0.01 0.01 0.05 0.08 0.14 0.7 Damage % 400 60% 30% 10% 5% 5% 3% 0% Claim Amount 240 120 40 20 20 12 0 (Claim - Mean) 231.72 111.72 31.72 11.72 11.72 3.72 -8.28 (Claim - Mean)^2 53694 12481 1006.2 137.36 137.36 13.838 68.558 Prob*(Claim - Mean)^2 536.94 124.81 10.062 6.8679 10.989 1.9374 47.991 Variance 739.6016 Std. Dev 27.195617

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Page 19 MODULE 3 NEIGHBORHOOD F Expected Value 2.805 Home Value (\$ thousands) Cat 5 Cat 4 Cat 3 Cat 2 Cat 1 TS None Probability 0.01 0.01 0.01 0.05 0.08 0.14 0.7 Damage % 150 50% 20% 10% 5% 5% 3% 0% Claim Amount 75 30 15 7.5 7.5 4.5 0 (Claim - Mean) 72.195 27.195 12.195 4.695 4.695 1.695 -2.805 (Claim - Mean)^2 5212.1 739.57 148.72 22.043 22.043 2.873 7.868 Prob*(Claim - Mean)^2 52.121 7.3957 1.4872 1.1022 1.7634 0.4022 5.5076 Variance 69.779475 Std. Dev 8.353411 NEIGHBORHOOD G Expected Value 1 Home Value (\$ thousands) Cat 5 Cat 4 Cat 3 Cat 2 Cat 1 TS None Probability 0.01 0.01 0.01 0.05 0.08 0.14 0.7 Damage % 100 25% 10% 10% 5% 2% 1% 0% Claim Amount 25 10 10 5 2 1 0 (Claim - Mean) 24 9 9 4 1 0 -1 (Claim - Mean)^2 576 81 81 16 1 0 1 Prob*(Claim - Mean)^2 5.76 0.81 0.81 0.8 0.08 0 0.7 Variance 8.96 Std. Dev 2.9933259
Page 20 MODULE 4 Module 4: Correlation and Regression In this module, students will learn about creating models to describe relationships between 2 quantitative variables. This will allow students to understand the relationship between hurricane damage amounts for homes based on distance from the ocean and other factors. Content Learning Objectives Through the use of historical data about hurricanes and Happy Shores, students will be able to do the following: ± Create scatterplots to describe 2-variable data.

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