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

Answer 2

The probability a loan application takes no longer than 12 days is 0.1666

• Range = 8 to 13 days
• Maximum number of days = 12

The probability a loan takes no longer than 12 days

Let x = time to process a loan application

for a uniform distribution (8, 13)

$f(x) = \frac{1}{6} ; 8 < x < 13$

The probability is

$Pr[x > 12] = \int\limits^1^3_1_2 {f(x)} \, dx = 1/6\int_1_2^1^3 dx = \frac{13-12}{6} = 1/6$

The probability a loan application takes no longer than 12 days is 0.1666

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