Question

In: Statistics and Probability

6.31. The exponential distribution can be used to solve Poisson-type problems in which the intervals are...

6.31. The exponential distribution can be used to solve Poisson-type problems in which the intervals are not time. The Air Travel Consumer Report published by the U.S. Department of Transportation reported that in a recent year, Virgin America led the nation in fewest occurrences of mishandled baggage, with a mean rate of 0.95 per 1,000 passengers. Assume that mishandled baggage occurrences are Poisson distributed. Using the exponential distribution to analyze this problem, determine the average number of passengers between occurrences. Suppose baggage has just been mishandled.

  1. What is the probability that at least 500 passengers will have their baggage handled properly before the next mishandling occurs?
  2. What is the probability that the number will be fewer than 200 passengers

Book says answers are

.μ = 1052.6

a..5908

b..1899 but how?

Solutions

Expert Solution

We know that the number of occurrence of events between two Poisson process follows exponential distribution.

Rate = 0.95/1000 per passengers = 0.00095 per passengers

Thus, the number of passengers will have their baggage handled properly (X) before the next mishandling occurs (Poisson process) foloow exponential distribution with rate parameter = 0.00095 per passengers

= 1/0.00095 = 1052.6 passengers

Probability that at least 500 passengers will have their baggage handled properly before the next mishandling occurs

= P(X 500) = exp(-0.00095 * 500)   P(X x) = exp(-x)

= 0.6219   

Probability that the number will be fewer than 200 passengers = P(X < 200)

= 1 - exp(-0.00095 * 200) P(X < x) = 1 - exp(-x)

= 1 - 0.8270

= 0.1730


Related Solutions

distinguish between the exponential distribution and the poisson distribution
distinguish between the exponential distribution and the poisson distribution
derive LR, LM and wald test for poisson and exponential distribution.
derive LR, LM and wald test for poisson and exponential distribution.
Prove that the Poisson distribution is in the exponential family of probability distributions given that the...
Prove that the Poisson distribution is in the exponential family of probability distributions given that the Poisson parameter is positive
Consider a Poisson distribution in which the offspring distribution is Poisson with mean 1.3. Compute the...
Consider a Poisson distribution in which the offspring distribution is Poisson with mean 1.3. Compute the (finite-time) extinction probabilities un = P{ Xn = 0 | X0 = 1 } for n = 0, 1, . . . , 5. Also compute the probability of ultimate extinction u∞.
(Exponential Distribution) The life, in years, of a certain type of electrical switch has an exponential...
(Exponential Distribution) The life, in years, of a certain type of electrical switch has an exponential distribution with an average life of ?? = 2 years. i) What is the probability that a given switch is still functioning after 5 years? ii) If 100 of these switches are installed in different systems, what is the probability that at most 30 fail during the first year?(also Binomial Distribution
The lifetime of a certain type of batteries follows an exponential distribution with the mean of...
The lifetime of a certain type of batteries follows an exponential distribution with the mean of 12 hours. a) What is the probability that a battery will last more than 14 hours? (Answer: 0.3114) b) Once a battery is depleted, it is replaced with a new battery of the same type. Assumingindependence between lifetimes of batteries, what is the probability that exactly 2 batteries will be depleted within 20 hours? (Answer: 0.2623) c) What is the probability that it takes...
Using I.uniform,II binomial , III. exponential and IV. Poisson random variable for each solve the following...
Using I.uniform,II binomial , III. exponential and IV. Poisson random variable for each solve the following A. What is the average of the 500 sample means when the sample size is n = 5? What is the average of the 500 sample means when the sample size is n = 50? What are the theoretical expected values of sample means, respectively? b. For n = 5 and n = 50, what are the variances of the 500 sample means, respectively?...
Reinsurance can be used by an insurance company to solve several problems. Assume you are an...
Reinsurance can be used by an insurance company to solve several problems. Assume you are an insurance consultant who is asked to give recommendations concerning the type of reinsurance plan or arrangement to use. For each of the following situations, indicate the type of reinsurance plan or arrangement that ceding insurer should use, and explain the reasons for your answer. Company ABC is an established homeowners insurer and is primarily interested in having protection against a catastrophic loss arising out...
Hardware Define the ways in which the system resources are used to solve the computing problems...
Hardware Define the ways in which the system resources are used to solve the computing problems of the users True or false. Operating system Controls and coordinates use of hardware among various applications and users True or false. A goal of the scheduling algorithms is to maximize CPU Utilization while minimizing Throughput True or false System and Application programs Provides basic computing resources True or false. The one program running at all times on the computer is the system True...
Q3. (a) The number of knots in a particular type of wood has a Poisson distribution...
Q3. (a) The number of knots in a particular type of wood has a Poisson distribution with an average of 1.5 knots in 0.28m3 of the wood. Find the probability that a 0.28m3 block of the wood has at most 1 knot. [3] (b) Cars arrive at a toll both according to a Poisson process with mean 80 cars per hour. If the attendant makes a one-minute phone call, what is the probability that at least 1 car arrives during...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT