Probability: expected value using exponential distribution

Please assist in answering the following question. Please submit details of work including excel sheet used to arrive to the solution. Provide interpretation of results and describe conclusions.

1. Suppose that a car rental agency offers insurance for a week that will cost $10 per day. A minor fender bender will cost $1,500, while a major accident might cost $15,000 in repairs. Without the insurance, you would be personally liable for any damages. What should you do? Clearly, there are two decision alternatives: take the insurance or do not take the insurance.

The uncertain consequences, or events that might occur, are that you would not be involved in an accident, that you would be involved in a fender bender, or that you would be involved in a major accident. Assume that you researched insurance industry statistics and found out that the probability of major accident is 0.05%, and that the probability of a fender bender is 0.16%. What is the expected value decision? Would you choose this? Why or why not? What would be some alternate ways to evaluate risk?

2. Suppose that the service rate to a waiting line system is 10 customers per hour (exponentially distributed). Analyze how the average waiting time is expected to change as the arrival rate varies from two to ten customers per hour (exponentially distributed).

Solution Summary

This solution is comprised of a detailed explanation of two probability questions using exponential distribution. This solution is comprised of calculations, formula and interpretation of results for both questions using the exponential distribution.

Someone purchases a liability insurance policy, and the probability that they will make a claim on that policy is equal to 0.1. The insurance payout is the amount of money the insurance company must pay if the holder of the policy files a claim. So, if no claim is made, then the insurance payout is just $0; however, whenever a c

1. The useful life of an electrical component is exponentially distrbuted with a mean of 2500 hours.
(a) what is the probability the circuit will last more than 3000 hrs.
(b) what is the probability the circuit will last between 2500 and 2750 hours
(c ) what is the probability the circuit will fail within the first 2000 hr

I've struggled for 3 days to come up with something approaching a relevant answer but am now desperate.
Could you solve Q3, both a) and b) parts from the Exercise Sheet attached?
Happy to pay 2 credits for both answers.
Thank you very much.
3. The random variable X has an exponentialdistribution with mean ยต. Let Y

Students in a class take a quiz with eight questions. The number x of questions answered correctly can be approximated by the following probability distribution. Complete parts (a) through (e).
X 0 1 2 3 4 5 6 7 8
P(x) 0.02 0.04 0.05 0.05 0.11 0.24

86. Give the z-score for a measurement from a normal distribution for the following:
a. 1 standard deviation above the mean
b. 1 standard deviation below the mean
c. equal to the mean
d. 2.5 standard deviations below the mean
e. 3 standard deviations above the mean
118. Suppose x is a binomial random vari

A consumer is contemplating the purchase of a new compact disc player. A consumer magazine reports data on the major brands. Brand A has lifetime (TA) which is exponentially distributed with m=.02; and Brand B has lifetime (TB) which is exponentially distributed with m=.01. (The unit of time is one year).
a. Find the expec

The Bureau of Labor Statistics' American Time Use Survey showed that the amount of time spent using a computer for leisure varied greatly by age. Individuals age 75 and over averaged .15 hour (9 minutes) per day using a computer for leisure. Individuals ages 15 to 19 spend 1.0 hour per day using a computer for leisure. If these

Please see attached file for full problem description.
The maintenance department of a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of two breakdowns every 500hours. Let x denote the time (in hours) between successive breakdowns.
a. Find lambda and mu(x)