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.

What is the mean time for the application process?

What is the likelihood a particular application will take less than 6 minutes?

What is the likelihood an application will take more than 5 minutes?

What is the mean time for the application process?

Explanation / Answer

a) The 'mean' is just a fancy word for the 'average'.
So the mean, (or halfway point) of 4 and 10 is:
(4 + 10) / 2 = 14 / 2 = 7
answer = 7 minutes

b) Since this is a uniform distribution centered with a mean of 7 minutes,
and since 99.7% of all observations fall within 3 standard deviations of the mean,
the standard deviation of the process time is:
(7 - 4) / 3 = 1
answer = 1 minute

c) The likelihood a particular application with take less than 6 minutes is:
100% - 50% - 34% = 16%

d)
answer = 2.5%

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