Question

The time between arrivals at a toll booth follows an exponential distribution with a mean time...

The time between arrivals at a toll booth follows an exponential distribution with a mean time between arrivals of 2 minutes.

What is the probability that the time between two successive arrivals will be less than 3 minutes?

What is the probability that the time will be between 3 and 1 minutes?

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

We are given the mean arrival time here as 2 minutes. Therefore the arrival time distribution here is given as:

a) The probability that the time is less than 3 minutes is computed here as:

Therefore 0.7769 is the required probability here.

b) The probability that the time will be between 3 and 1 minutes is computed here as:

Therefore 0.3834 is the required probability here.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The time between successive arrivals of calls to emergency service is random variable which follows exponential...
The time between successive arrivals of calls to emergency service is random variable which follows exponential distribution. It was observed that on average calls arrive to emergency service every four minutes (1 / λ = 4min) and average number of calls in one minute is λ = 0.25 calls/ 1 min The probability that the time between successive calls is less than 2 minutes is ______ A call just arrived to emergency service. The probability that next call will arrive...
The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with...
The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 10 seconds. (a) Sketch this exponential probability distribution. (b) What is the probability that the arrival time between vehicles is 10 seconds or less? (Round your answer to four decimal places.) (c) What is the probability that the arrival time between vehicles is 4 seconds or less? (Round your answer to four decimal places.) (d) What is the probability of 30...
2. The waiting time between arrivals at a Wendy’s drive-through follows an exponential distribution with ?...
2. The waiting time between arrivals at a Wendy’s drive-through follows an exponential distribution with ? = 15 minutes. What is the distribution of the number of arrivals in an hour? a. Poisson random variable with μ=15 b. Poisson random variable with μ=4 c. Exponential random variable with ?=15 d. Exponential random variable with ?=4
Suppose that the time between successive occurrences of an event follows an exponential distribution with mean...
Suppose that the time between successive occurrences of an event follows an exponential distribution with mean number of occurrences per minute given by λ = 5. Assume that an event occurs. (A) Derive the probability that more than 2 minutes elapses before the occurrence of the next event. Derive the probability that more than 4 minutes elapses before the occurrence of the next event. (B) Use to previous results to show: Given that 2 minutes have already elapsed, what is...
Let X = the time between two successive arrivals at the drive-up window of a local...
Let X = the time between two successive arrivals at the drive-up window of a local bank. Suppose that X has an exponential distribution with an average time between arrivals of 4 minutes. a. A car has just left the window. What is probability that it will take more than 4 minutes before the next drive-up to the window? b. A car has just left the window. What is the probability that it will take more than 5 minutes before...
The time between telephone calls to a cable televisiom service call center follows an exponential distribution...
The time between telephone calls to a cable televisiom service call center follows an exponential distribution with a mean of 1.5 minutes. a. What is the probability that the time between the next two calls will be 48 seconds or less? b. What is the probability that the between the next two calls will be greater than 118.5 seconds?
Let X = the time between two successive arrivals at the drive-up window of a local...
Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with λ=1, compute the following: a) The expected time between two successive arrivals b) The standard deviation of the time between success arrivals c) Calculate the probability P (X≤3) d) Calculate the probability P(2≤X≤5)
Customers arrive at random times, with an exponential distribution for the time between arrivals. Currently the...
Customers arrive at random times, with an exponential distribution for the time between arrivals. Currently the mean time between customers is 6.34 minutes. a. Since the last customer arrived, 3 minutes have gone by. Find the mean time until the next customer arrives. b. Since the last customer arrived, 10 minutes have gone by. Find the mean time until the next customer arrives.
1. The process time of oil change in a car follows an exponential distribution with a...
1. The process time of oil change in a car follows an exponential distribution with a mean of 5 minutes. What is the probability that a process of oil change takes more than 6 minutes? 2. What is the probability that a process of oil change takes between 3 and 5 minutes?
Let X be the time between successive arrivals to an intersection in a rural area. Suppose...
Let X be the time between successive arrivals to an intersection in a rural area. Suppose cars arrive to the intersection via a Poisson process at a rate of 1 every 5 minutes. (a) What distribution does X have? (b) What is the mean time between arrivals? (c) What is the probability that more than 7 minutes will pass between arrivals to the intersection?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT