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

Organized list strategy, i can not figer out my homework it says "USE THE M...

i can not figer out my homework it says "USE THE MAKE AN ORGANIZED LIST STRATEGY,Medeline bikes 4 laps around her neighborhood 2 times a week.How many laps does she bike in 8 weeks

Probability, I have a question that hurts my head to work out. It is really...

I have a question that hurts my head to work out. It is really confusing for me. It sais " By the start of the 21st century, only 1 in 6 babies in America was born with blue eyes.

Homogeneous system , Provided a homogeneous system of equations (2), we wil...

Provided a homogeneous system of equations (2), we will have one of the two probabilities for the number of solutions. 1.   Accurately one solution, the trivial solution 2.

..percentage, how to express 15/4 into percentage

how to express 15/4 into percentage

Calculate the score of contestant on a tv game show, Danny is a contestant ...

Danny is a contestant on a TV game show. If he gets a question right, the points for that question are added to his score. If he gets a question wrong, the points for that question

Confidence interval, Confidence Interval The interval estimate or a 'co...

Confidence Interval The interval estimate or a 'confidence interval' consists of a range as an upper confidence limit and lower confidence limit whether we are confident that a

Show that the vector is in the perfect matching polytope, 1.  Let G = (V,E)...

1.  Let G = (V,E) be a graph for which all nodes have degree 5 and where G is 5-edge is connected. a) Show that the vector x which is indexed by the edges E and for which x e =

The ratio of boys to girls at the dance was 3:4, The ratio of boys to girls...

The ratio of boys to girls at the dance was 3:4. There were 60 girls at the dance. How many boys were at the dance? Use a proportion comparing boys to girls at the dance. Boys/

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