Find out the mean wait in line - probability, Mathematics

Assignment Help:

Example of Probability

Illustration:  It has been determined that the probability density function for the wait in line at a counter is specified by,

691_Find out the mean wait in line - Probability 1.png

In which t is the number of minutes spent waiting in line. Solve each of the following questions concerning to this probability density function.

(a) Prove that this is in fact a probability density function.

(b) Find out the probability that a person will wait in line for at least 6 minutes.

(c) Find out the mean wait in line.

Solution

(a) Prove that this is in fact a probability density function.  

This function is evidently positive or zero and so there is not much to do here other than calculate the integral.

2027_Find out the mean wait in line - Probability 2.png

Thus it is a probability density function.  

(b) Find out the probability that a person will wait in line for at least 6 minutes. The probability that we're searching for here is P (x > 6).

2430_Find out the mean wait in line - Probability 3.png

Thus the probability that a person will wait in line for much more than 6 minutes is 54.8811%.

(c) Find out the mean wait in line. 

 Here is the mean wait time.

1043_Find out the mean wait in line - Probability 4.png

Thus, it looks like the average wait time is 10 minutes.


Related Discussions:- Find out the mean wait in line - probability

Probability questions, The probability that a person will get an electric c...

The probability that a person will get an electric contract is 2/5 and the contract that he will not get plumbing  contract is 4/7.If the probability of getting at least one contra

Linear equation in two variables., draw the graph of following pair of line...

draw the graph of following pair of linear equation:-2y=4x-6

Skewness-measure of central tendency, Skewness - It is a concept which...

Skewness - It is a concept which is normally used in statistical decision making. This refers to the degree whether a described frequency curve is deviating away from the gene

Technique of teching, What is a review technique? What are its advantages a...

What is a review technique? What are its advantages and disadvantages?

Approximating solutions to equations newtons method, Approximating solution...

Approximating solutions to equations : In this section we will look at a method for approximating solutions to equations. We all know that equations have to be solved on occasion

Simulation model, Thorwarth M., Arisha, A. and Harper P., (2009) Simulation...

Thorwarth M., Arisha, A. and Harper P., (2009) Simulation model to investigate flexible workload management for healthcare and servicescape environment, Proceedings of the 2009 Win

Estimate how much did the budget increase, Previous year's budget was 12.5 ...

Previous year's budget was 12.5 million dollars. This year's budget is 14.1 million dollars. How much did the budget increase? Last year's budget must be subtracted from this y

Quadratic equation whose roots are real, Write the quadratic equation whose...

Write the quadratic equation whose roots are real and non conjugate Ans)  x^2-x+6=0 ...roots are real and non conjugate

Markov chain, The Video Club Martin rents movies at "regular price" andat ...

The Video Club Martin rents movies at "regular price" andat "half price". Usually if the films are regularly priced one day, they will be at regular price the next day with probab

Find out the total number people and the total number car, A national park ...

A national park remains track of how many people per car enter the park. Today, 57 cars had 4 people, 61 cars had 2 people, 9 cars had 1 person, and 5 cars had 5 people. What is th

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd