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

Geometry, prove angle MJL is congruent to angle KNL

prove angle MJL is congruent to angle KNL

Childrens errors are a natural and inevitable part, Childrens errors are a ...

Childrens errors are a natural and inevitable part of their process of learning. In the process of grasping new concepts, children apply their existing understanding, which may

Method of cylinders or method of shells, Method of cylinders or method of s...

Method of cylinders or method of shells The formula for the area in all of the cases will be,                                                        A = 2 ∏ ( radius ) (heig

Multiplication of two matrices, Need assignment help, Explain Multiplicatio...

Need assignment help, Explain Multiplication of two Matrices.

Explain histogramsin details, Explain Histogramsin details? Another way...

Explain Histogramsin details? Another way to display frequencies is by using a histogram. The following is an example of a histogram using the data from the previous example:

Decision theory, Decision Theory Decisions There are many types of ...

Decision Theory Decisions There are many types of decision making 1.      Decision making under uncertainty It refer to situations where more than one outcome can r

Polynomials, On dividing p(X)=5x^(4)-4x^(3)+3x^(2)-2x+1 by g(x)=x^(2)+2 if ...

On dividing p(X)=5x^(4)-4x^(3)+3x^(2)-2x+1 by g(x)=x^(2)+2 if q(x)=ax^(2)+bx+c, find a,b and c.

ALJEBRA, HOW TO FIND 2SQUARE *7 CUBE

HOW TO FIND 2SQUARE *7 CUBE

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