Question

A daily mail is delivered to your house between 1:00 p.m. and 5:00 p.m. Assume delivery times follow the continuous uniform distribution. Determine the percentage of mail deliveries that are made after 4:00 p.m.

Answer 1

Answer:

25% of deliveries

Step-by-step explanation:

This is a uniform distribution with parameters a = 1.00 and b =5.00. With these conditions, the following probability distribution functions can be applied:

$P(X \leq x)=\frac{x-a}{b-a}=\frac{x-1.00}{5.00-1.00}\\P(X \leq x) = \frac{x-1}{4}\\P(X \geq x) = 1- P(X \leq x) \\P(X \geq x)=1- \frac{x-1}{4}$

Therefore, the probability that X ≥ 4:00 p.m. is given by

$P(X \geq 4)=1- \frac{4-1}{4}\\P(X \geq 4)=0.25=25\%$

Thus, 25% of deliveries are made after 4:00 p/m.