Suppose the time to process a loan follows a uniform distribution over 5 to 14 days. What is the probability that a loan takes longer than 8 days to process?

Question

I am in applied statistics which is a Math 201 course in college. I don't understand this chapter.

Answer 1

Amanda:

 

Let Y be the time to process a loan.  We are given that Y follows a (I am assuming to be CONTINUOUS) unifrom distribution over the interval of 5 to 14 days. The probability density curve here is a straight line (uniform distribution). The area under any probability density has to be 1 (100%). Here, iImagine a rectangle of base 14-5 = 9.  If the area of the rectangle has to be one, what should be its height?  Think.  The height should be 1/ 9 right?  Right.

 

The required probability, P[Y>8] is just the area under the curve to the right of 8.  The portion of the base to the right of 8 is 14-8 = 6.  The area of this portion is 8(1/9) = 8/9.  Done.

 

Amanda, if you regard your time to process the loan, as NUMBER of days, the variable is discrete, taking values, 5, 6, 10,..., 14.  These are (COUNT.......)  TEN values.  Now we have a discrete probability MASS FUNCTION, (not a curve, but "sticks"), each of height 1/10 at each value to make the total mass10(1/10) = 1.   You need P{Y> 8]  (Note: longer than 8 days means 9 or more days, See the difference between a discrete and a continuous variable.)

These are (count, 9., 10, ...14) SIX values.  So the answer now is 6(1/10) = 6/10.  NOT 8/9. 

 

This the difference that your assumption (whether continuous uniform or discrete uniform) makes.

 

Which assumption would you rather make? Are the loans processed and sanctioned continuously or on a daily basis?  Post a comment.

 

Dr. G.