Many retail stores offer their own credit cards. At the time of the credit appli

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? Standard deviation (c) What is the likelihood a particular application will take less than 6 minutes? Probability (d) What is the likelihood an application will take more than 5 minutes? Probability

Explanation / Answer

PDF of Uniform Distribution f(x) = 1 / ( b - a ) for a < x < b
b = Maximum Value
a = Minimum Value
Mean = a + b / 2
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 )
a.
Mean = a + b / 2 = 7

b.
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 ) = 1.732
f(x) = 1/(b-a) = 1 / (10-4) = 1 / 6 = 0.1667
c.
P(X < 6) = (6-4) * f(x)
= 2*0.1667
= 0.333
d.
P(X > 5) = (10-5) * f(x)
= 5*0.1667
= 0.834
To find P(a < X < b) =( b - a ) * f(x)
P(0.8 < X < 0.88) = (0.88-0.8) * f(x)
= 0.08*0.1667
= 0.013

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