Question

Your insurance company has converged for three types of cars. The annual cost for each type of cars can be modeled using Gaussian (Normal) distribution, with the following parameters: (Discussions allowed!)

• Car type 1 Mean=$520 and Standard Deviation=$110

• Car type 2 Mean=$720 and Standard Deviation=$170

• Car type 3 Mean=$470 and Standard Deviation=$80

Use Random number generator and simulate 1000 long columns, for each of the three cases. Example: for the Car type 1, use Number of variables=1, Number of random numbers=1000, Distribution=Normal, Mean=520 and Standard deviation=110, and leave random Seed empty.

Next: use either sorting to construct the appropriate histogram or rule of thumb to answer the questions:

13. What is approximate probability that Car Type 3 has annual cost less than $550?

• a. Between 1% and 3%

• b. Between 27% and 39%

• c. Between 75% and 90%

• d. None of these

14. Which of the three types of cars is most likely to cost less than $400?

• a. Type 1

• b. Type 2

• c. Type 3

15. For which of the three types we have the highest probability that it will cost between $500 and $700?

• a. Type 1

• b. Type 2

• c. Type 3

Answer 1

13. What is approximate probability that Car Type 3 has annual cost less than $550?

Mean=$470

Standard Deviation=$80

P(X < 550) = (550 - 470)/80 = 1

The p-value is 0.8413 or 84.13%.

The answer is c. Between 75% and 90%

14. Which of the three types of cars is most likely to cost less than $400?

For Car type 1:

Mean=$520

Standard Deviation=$110

P(X < 400) = (400 - 520)/110 = -1.09

The p-value is 0.1377 or 13.77%.

For Car type 2:

Mean=$720

Standard Deviation=$170

P(X < 400) = (400 - 720)/170 = -1.88

The p-value is 0.0299 or 2.99%.

For Car type 3:

Mean=$470

Standard Deviation=$80

P(X < 400) = (400 - 470)/80 = -0.875

The p-value is 0.1908 or 19.08%.

The answer is c. Type 3

15. For which of the three types we have the highest probability that it will cost between $500 and $700?

For Car type 1:

Mean=$520

Standard Deviation=$110

P(500 < X < 700) = P(Z = (700 - 520)/110) - P(Z = (500 - 520)/110) = P(Z = 1.64) - P(Z = -0.18)

The p-value is 0.9491 - 0.4279 = 0.5213 or 52.13%.

For Car type 2:

Mean=$720

Standard Deviation=$170

P(500 < X < 700) = P(Z = (700 - 720)/170) - P(Z = (500 - 720)/170) = P(Z = -0.12) - P(Z = -1.29)

The p-value is 0.4532 - 0.0978 = 0.3554 or 35.54%.

For Car type 3:

Mean=$470

Standard Deviation=$80

P(500 < X < 700) = P(Z = (700 - 470)/80) - P(Z = (500 - 470)/80) = P(Z = 2.88) - P(Z = 0.38)

The p-value is 0.9980 - 0.6462 = 0.3518 or 35.18%.

The answer is a. Type 1