Chapter 6.1, Problem 24E

To determine

To find: the probability for between 2 and 5 minutes.

Answer to Problem 24E

  $\text{P}\left(2<X<5\right)=0.375$

Explanation of Solution

Formula used:

Density curve for the uniform distribution

  $f\left(x\right)=\frac{1}{a-b}$

Calculation:

Interval from 0 to 8

  $\begin{array}{c}a=0\\ b=8\end{array}$

Density curve for the uniform distribution

  $\begin{array}{c}f\left(x\right)=\frac{1}{8-0}\\ =\frac{1}{8}\\ =0.125\end{array}$

  $0\le x\le 8$

Probability for between 2 to 5 minutes

  $\begin{array}{c}\text{P}\left(2<X<5\right)=(5-2).\frac{1}{8}\\ =3.\frac{1}{8}\\ =0.375\\ 37.5\%\end{array}$