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The total time to process a loan application is uniformly distributed between 9 and 15 days.
What is the probability that a loan will be processed in 12 days or less?
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To answer the question, first calculate the duration of the time interval [9,12] days :
it is 12-9 = 3 days.
Next calculate the duration of the base time interval [9,15] days :
it is 15-9 = 6 days.
Last step is to compute the ratio of the shorter time interval to the base time interval
P = = = 0.5 = 50%. ANSWER
Solved.
It is how the uniform probability distribution works.