Question

The Harbour Island Ferry leaves on the hour and at 15-minute intervals. The time, x, it takes John to drive from his house to the ferry has a uniform distribution with x between 10 and 20 minutes. One morning John leaves his house at precisely 9:00 A.M. a. What is the probability John will wait less than 4 minutes for the ferry?

Answer 1

ANSWER

$0.4$

EXPLANATION

The Harbor Island Ferry leaves on the hour and at 15-minute intervals.

It takes John to drive from his house to the ferry has a uniform distribution with x between 10 and 20 minutes.

The probability distribution graph is a rectangle with a base of 10 to 20 as shown below:

The rectangle's height will be 1/10 because its area equals the whole probability i.e.:

$\begin{gathered} \frac{1}{20-10} \\ \\ \frac{1}{10} \end{gathered}$

We need to find the area based on the specified endpoints to find the probability.

If John waits less than 4 minutes for the ferry, it implies that he arrives between 9:11 and 9:15 am. Therefore, we have to find the area of the rectangle that has a height of 1/10 and a width of 4:

$\begin{gathered} P=4*\frac{1}{10} \\ \\ P=0.4 \end{gathered}$

That is the probability.