Question

Assume a random variable representing the amount of time it takes for a customer service representative to pick up has a uniform distribution between 15 and 20 minutes. What is the probability that a randomly selected application from this distribution took less than 18 minutes

Answer 1

Answer:

0.6 = 60% probability that a randomly selected application from this distribution took less than 18 minutes.

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.  

The probability of finding a value of at lower than x is:

$P(X < x) = \frac{x - a}{b - a}$

The probability of finding a value between c and d is:

$P(c \leq X \leq d) = \frac{d - c}{b - a}$

The probability of finding a value above x is:

$P(X > x) = \frac{b - x}{b - a}$

Uniform distribution between 15 and 20 minutes.

This means that $a = 15, b = 20$

What is the probability that a randomly selected application from this distribution took less than 18 minutes?

$P(X < 18) = \frac{18 - 15}{20 - 15} = 0.6$

0.6 = 60% probability that a randomly selected application from this distribution took less than 18 minutes.