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Solved: An automobile insurance company divides customers

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 20E Chapter 2.3

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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21
1
Problem 20E

An automobile insurance company divides customers into three categories, good risks, medium risks, and poor risks Assume that 70% Of tfl6 customers are good risks, 20% are medium risks, and 10% are poor risks. Assume that during the course of a year, a good risk customer has probability 0.005 of filing an accident claim, a medium risk customer has probability 0.01, and a poor risk customer has probability 0.025. A customer is chosen at random.

a. What is the probability that the customer is a good risk and has filed a claim?

b. What is the probability that the customer has filed a claim?

c. Given that the customer has filed a claim, what is the probability that the customer is a good risk?

Step-by-Step Solution:
Step 1 of 3

Solution 20E

Step1 of 3:

We have an automobile insurance company it divides customers into three categories they are

1).Good risk(G)  

2).Medium risk(M)

3).Poor risk(P).

Also we have,

P(Good risk) = 70%

                     = 0.70

P(Medium risk) = 20%

                          = 0.20

P(Poor risk) = 10%

                    = 0.1

P(Claim/Good risk) = 0.005

P(Claim/Medium risk) = 0.01

P(Claim/Poor risk) = 0.025

We need to find,

a).We need to find the probability that the customer is a good risk and has filed a claim?

b).We need to find the probability that the customer has filed a claim?

c).We need to find the probability that the customer is a good risk? When customer has filed a claim,

Step2 of 3:

a).

The probability that the customer is a good risk and has filed a claim is given by

         P(The probability that the customer is a good risk and has filed a claim) = P(GC)

                                                                                                                            =

                                                                                                                       =                                                                                                      

                                                                                                             = 0.0035

Therefore, The probability that the customer is a good risk and has filed a claim is 0.0035.


b).

The probability that the customer has filed a claim, is given by

 P(The probability that the customer has filed a claim) = P(C)

                                                                                     = P(GC) + P(MC) + P(PC)   .....(1)

Where

P(GC) =          

         =

                                                                      = 0.0035

  Hence, P(GC) = 0.0035

Now

P(MC) =

      =

                                                                     = 0.002

Hence, P(MC) = 0.002 and

P(PC) =

      =

                                                                     = 0.0025

Hence, P(PC) = 0.0025.

Substitute these values in equation (1) we get

P(C) = P(GC) + P(MC) + P(PC)

                                                        = 0.0035 + 0.002 + 0.0025

                                                        = 0.008

Therefore, The probability that the customer has filed a claim is 0.008.


Step3 of 3:

c).

The probability that the customer is a good risk is given by

P(The probability that the customer is a good risk) = P(G/C)

                                                                      =

                                                                      =  

 [= 0.0035 from part(a) and P(C) = 0.008 from part(b)]

                                                                      = 0.4375

Therefore, The probability that the customer is a good risk is 0.4375.


Conclusion:

a).The probability that the customer is a good risk and has filed a claim is 0.0035.

b).The probability that the customer has filed a claim is 0.008.

c).The probability that the customer is a good risk is 0.4375.

 

 

Step 2 of 3

Chapter 2.3, Problem 20E is Solved
Step 3 of 3

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

Since the solution to 20E from 2.3 chapter was answered, more than 1912 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The answer to “An automobile insurance company divides customers into three categories, good risks, medium risks, and poor risks Assume that 70% Of tfl6 customers are good risks, 20% are medium risks, and 10% are poor risks. Assume that during the course of a year, a good risk customer has probability 0.005 of filing an accident claim, a medium risk customer has probability 0.01, and a poor risk customer has probability 0.025. A customer is chosen at random.a. What is the probability that the customer is a good risk and has filed a claim?________________b. What is the probability that the customer has filed a claim?________________c. Given that the customer has filed a claim, what is the probability that the customer is a good risk?” is broken down into a number of easy to follow steps, and 121 words. The full step-by-step solution to problem: 20E from chapter: 2.3 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This full solution covers the following key subjects: customer, Probability, risks, Risk, good. This expansive textbook survival guide covers 153 chapters, and 2440 solutions.

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Solved: An automobile insurance company divides customers