Question

In: Statistics and Probability

Your insurance company has converged for three types of cars.The annual cost for each type...

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

Solutions

Expert Solution

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


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