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

External division of section formula, give me the derivation of external di...

give me the derivation of external division of sectional formula using vectors

Integers, What are some equations for 36?

What are some equations for 36?

How many square centimeters are in one square meter, How many square centim...

How many square centimeters are in one square meter? There are 100 cm in a meter. A square meter is 100 cm through 100 cm. The area of this is 10,000 sq cm (100 × 100 = 10,000)

Linear approximation method for interpolation, Linear Approxi...

Linear Approximation Method This is a rough and ready method of interpolation and is best used when the series moves in predicted interval

Show that the height of the opposite house, From a window x meters hi...

From a window x meters high above the ground in a street, the angles of elevation and depression of the top and the foot of the other house on the opposite side of the street  are

Find out the mean wait in line - probability, Example of Probability I...

Example of Probability Illustration:  It has been determined that the probability density function for the wait in line at a counter is specified by, In which t is the

Trigonometry, how to work out consumer arithmetic?

how to work out consumer arithmetic?

Geometry, what are the parts of angles

what are the parts of angles

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