Question

Bob 's daily commute time is randomly distributed with a minimum of 20 minutes, a maximum of 61 minutes, and the most common length is 30 minutes. What is the probability that his commute today took more than 35 minutes?

Answer 1

Answer:

0.6341 = 63.41% probability that his commute today took more than 35 minutes

Step-by-step explanation:

Randomly distributed = Uniform distribution.

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distributon has two bounds, a and b, and the probability of finding a value higher than x is given by:

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

Randomly distributed with a minimum of 20 minutes, a maximum of 61 minutes.

This means that $a = 20, b = 61$.

What is the probability that his commute today took more than 35 minutes?

$P(X > 35) = \frac{61 - 35}{61 - 20} = 0.6341$

0.6341 = 63.41% probability that his commute today took more than 35 minutes