Question

Many retail stores offer their own credit cards. At the time of the credit application, the customer is given a 10% discount on the purchase. The time required for the credit application process follows a uniform distribution with the times ranging from 4 minutes to 10 minutes.

a.	What is the mean time for the application process?

Mean

  

b.	What is the standard deviation of the process time? (Round your answer to 3 decimal places.)

Standard deviation

  

c.	What is the likelihood a particular application will take less than 6 minutes? (Round your answer to 4 decimal places.)

Probability

   

d.	What is the likelihood an application will take more than 5 minutes? (Round your answer to 4 decimal places.)

Probability

Answer 1

Answer :

given data :-

the customer is given a discount on the purchase =10%

uniform distribution with the times ranging from 4 minutes to 10 minutes.

let we take

a = 4

b = 10

(a). the mean time for the application process

the mean time of any uniform distribution is the midpoint between the points a and b,

here its = ( b+a )/2

= (10+4)/2

= 7

(b). the standard deviation of the process time

the variance of a uniform dist is (b-a)^2 / 12 and the s.d is the square root of the variance therefore (b-a)/sqrt(12)

= (10-4)/sqrt(12)

= 6/3.464

= 1.73

(c).the likelihood a particular application will take less than 6 minutes

this would be the area under the graph before 6. in other words,

the area of the rectangle whose base is from 4 to 6 and height is = 1/6

= 0.166

= 16.66%

(d). the likelihood an application will take more than 5 minutes

this is the area under the graph after 5,

area of a rectangle whose base is between 5 and 10, and height is 1/6