Chapter 6.1, Problem 23E

To determine

To find: the probability for less than 300 seconds.

Answer to Problem 23E

  $\text{P}\left(X<300\right)=0.0833$

Explanation of Solution

Formula used:

Density curve for the uniform distribution

  $f\left(x\right)=\frac{1}{a-b}$

Calculation:

Interval from 0 to 300 (in seconds)

  $\begin{array}{c}a=0\\ b=300\end{array}$

Density curve for the uniform distribution

  $\begin{array}{c}f\left(x\right)=\frac{1}{a-b}\\ =\frac{1}{3600-0}\\ =\frac{1}{3600}\end{array}$

  $0\le x\le 300$

Probability for less than 5 minute (300 seconds)

  $\begin{array}{c}\text{P}\left(X<300\right)=(300-0).\frac{1}{3600}\\ =\frac{300}{3600}\\ =0.0833\\ 8.33\%\end{array}$