BEM-5-Insurance

BEM-5-Insurance - Page Text Content

FC: Bridget Murphy | F. Bender's Insurance Agency SENIOR CITIZEN'S ACCIDENT POLICY

1: 5.) Suppose that you are an actuary for F. Bender's Insurance Agency. Your company plans to offer a senior citizen's accident policy, and you must predict the likelihood of an accident as a function of the driver's age. From previous accident records, you find the following information: | AGE (years) 20 30 40 | Accidents per 100 Million Km Driven 440 280 200

2: Write an equation expressing accidents per 100 million kilometers in term of age. | Step 1- STAT-> 1:Edit -> enter data *make sure stat plot 1 is turned on Step 2- STAT -> CALC-> 5: QuadReg -> enter

3: accidents per 100 million Km driven = .4x^2 - 36x + 1000 | Step 3- make an equation using the variables given:

4: How many accidents per 100 million kilometers would you expect for an 80-year-old driver? | I would expect an 80-year-old driver to be in 680 accidents every 100 million kilometers. | 2nd Graph: scroll to x=80 to find the accident expectancy in column Y1

5: Based on your model, who is safer; a 16-year-old driver or a 70-year-old driver? | Based on my model, a 70-year-old driver is safer than a 16-year-old driver because the data shows a 70-year-old has approximately 440 accidents per 100 million Km driven while a 16-year-old has approximately 526 accidents per 100 million Km driven. | Then, scroll on the same page so that x= 70 and x=16 and compare the Y1 values.

6: What age driver appears to be the safest? | A 45-year-old driver appears to be the safest because the data shows that they have approximately 190 accidents per 100 million Km driven which is lower than all other ages. | Step 1: still on the table, scroll until the Y values decrease and begin to increase again. The X value to the left of the smallest Y value is the answer.

7: Your company decides to insure licensed drivers up to the age where the accident rate reaches 830 per 100 million kilometers. What, then, is the domain of this quadratic function? | The domain is (5, 85) | Find the lowest and highest X values which have Y values of 830 accidents per 100 million Km driven.