Suppose that the service time at a store with only, one check-out counter is Exponentially distributed,...

Suppose that the service time at a store with only, one check-out counter is Exponentially distributed, with a mean time of 10 minutes.

a) What is the probability that a customer who is first in line now will spend more than 15 minutes waiting in the check-out line? (Solve using Exponential distribution and then using Poisson.)

b) A customer has already been waiting in the line for more than 10 minutes. What is the probability that this customer will still be at the store in more than 15 minutes from now?

c) What is the probability of spending less than a half an hour at the check-out? (Solve using two different time units.)

Solutions

Expert Solution

It is given that the service time at a store with only, one check-out counter is Exponentially distributed, with a mean time of 10 minutes. The PDF is .

a) The required probability is

The Poisson equivalent is no one person arrive in the first 15 minutes. Here .

The number of persons in 15 minutes has distribution .

The required probability is

b) The required conditional probability is

c) The required probability is

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Suppose the life time of a certain brand of light bulbs is exponentially distributed with an...

Suppose the life time of a certain brand of light bulbs is exponentially distributed with an average of 1000 hours. a. What’s the probability that a new light bulb won’t be able to reach this amount of time? b. What’s the probability that a new light bulb will have a life between 1000 and 2000 hours? c. Given that a light bulb has been working for 1000 hours, what’s the probability that it can work for another 2000 hours or...

Suppose the amount of time to finish assembling a component is exponentially distributed with an average...

Suppose the amount of time to finish assembling a component is exponentially distributed with an average of 2 minutes. (a) What is the probability that it takes more than 5 minutes to assemble a component? (b) If 100 components are randomly selected, what is the probability that the average amount of time to assemble these100 components is more than 2.3 minutes?

The average length of time customers spent on waiting at ABC Store’s check-out counter before a...

The average length of time customers spent on waiting at ABC Store’s check-out counter before a new P.O.S. system was installed was 4.3 minutes. A sample of 40 customers randomly selected at the check-out counter after the new P.O.S. system was installed showed that the average waiting time was 3.5 minutes with a sample standard deviation of 2.8 minutes. We wish to determine if the average waiting time after the P.O.S. system was installed is less than 4.3 minutes. 1. State...

Suppose you own three computers, each of which independently lasts for an exponentially distributed time with...

Suppose you own three computers, each of which independently lasts for an exponentially distributed time with a mean of 4 years. Let X(t) be the number of these computers that have broken down after t years. (a) What is the probability that all three computers are still working after six months? (b) On average, how long will it take before there is only one working computer left?

Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers...

Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 16 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 20 customers per hour. The manager’s service goal is to limit the waiting time prior to beginning the checkout process to no more than five minutes. Also the manager of...

Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers...

Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 13 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 20 customers per hour. The manager’s service goal is to limit the waiting time prior to beginning the checkout process to no more than five minutes. Also the manager of...

the time between phone calls received by a telephonist is exponentially distributed with a mean of...

the time between phone calls received by a telephonist is exponentially distributed with a mean of 10 minutes.what is the probability that there are no more than four calls within one hour?

In a grocery store, there is one cashier counter. Customers arrive at the cashier counter according...

In a grocery store, there is one cashier counter. Customers arrive at the cashier counter according to a Poisson process. The arrival rate is 30 customers per hour. The service time is exponentially distributed. The mean service time is 1 minute 30 seconds. What is the expected waiting time?

Suppose hard drive A has a lifetime that is exponentially distributed with mean of 6 years...

Suppose hard drive A has a lifetime that is exponentially distributed with mean of 6 years and hard drive B has a lifetime that is exponentially distributed with a mean of 2 years. What is the probability that drive B lasts at least 3 times longer than drive A?

The time T between requests to a web server is exponentially distributed with mean 0.5 seconds....

The time T between requests to a web server is exponentially distributed with mean 0.5 seconds. (a) What is the value of the parameter in this exponential distribution? Give the p.d.f. and c.d.f. of T? [2] (b) Use the c.d.f. of T to find the median request time and interpret it. [3] (c) What is the probability that the request time is between 0.25 and 1.5 seconds? [1]( d) Find the 60th percentile of the request time and interpret it....

Subjects