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:

Given that:

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.

use uniform distribution,to calculate probability

Let X = Bob's daily commute time

X Uniform (20,16)

For X to be uniform distribution with range (a,b) then cdf (F(x)) = P(X X) = (X-a)/b-a

Here we want

P(X>35) = 1-P(X 35)

= 1 - ((35-20)/(61-20))

= 1 - (15 /41)

= 1 - 0.3658

= 0.6341

The required probability is 0.6341