Q:

# 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?

Accepted Solution

A:
Answer: 0.2Step-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