Question

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

• 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 the 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 1 has an annual cost less than $350?

• a. Between 1% and 3%
• b. Between 3% and 9%
• c. Between 10% and 15%
• d. None of these

14. Which of the three types of cars is least likely to cost less than $350?

• a. Type 1
• b. Type 2
• c. Type 3

15. For which of the three types we expect that (approximately) 95% of cases will be between $300 and $740?

• a. Type 1
• b. Type 2
• c. Type 3

Task 3

Answer 1

13. What is approximate probability that Car Type 1 has an annual cost less than $350?

The following information has been provided:

We need to compute. The corresponding z-value needed to be computed:

Therefore,

b. Between 3% and 9%

14. Which of the three types of cars is least likely to cost less than $350?

The car with maximum mean and standard deviation is least likely to cost less than $350

The correct answer is type 2

15. For which of the three types we expect that (approximately) 95% of cases will be between $300 and $740?

Simplest way to check is to obtain the middle value of the interval, the car with middle value of the interval = mean will be the answer

( 300 + 740 )/2= 1140/2 = 520

a. Type 1