Question

Suppose the time to process a loan application follows a uniform distribution over the range of 8 to 13 days. What is the probability that a randomly selected loan application takes longer than 12 days to process?

Answer 1

Answer: 0.2

Step-by-step explanation:

We know that , the probability density function for uniform distribution is given buy :-

$f(x)=\dfrac{1}{b-a}$, where x is uniformly distributed in interval [a,b].

Given : The time to process a loan application follows a uniform distribution over the range of 8 to 13 days.

Let x denotes the time to process a loan application.

So the probability distribution function of x for interval[8,13] will be :-

$f(x)=\dfrac{1}{13-8}=\dfrac{1}{5}$

Now , the probability that a randomly selected loan application takes longer than 12 days to process will be :-

$\int^{13}_{12}\ f(x)\ dx\\\\=\int^{13}_{12}\dfrac{1}{5}\ dx\\\\=\dfrac{1}{5}[x]^{13}_{12}\\\\=\dfrac{1}{5}(13-12)=\dfrac{1}{5}=0.2$

Hence, the probability that a randomly selected loan application takes longer than 12 days to process = 0.2