Question

If $X$ is the waiting time in minutes for bus and p. d. f of $X$ is given by

$f\left(x\right)=\begin{array}{l}\left\{\begin{array}{cc}\frac{1}{5}& 0\le x\le 5\\ 0& otherwise\\ & \end{array}\right.\end{array}$

then probability of waiting time not more than $4$ minutes is

• A. $0.3$
• B. $0.8$
• C. $0.2$
• D. $0.5$

Answer 1

The correct option is B

$0.8$

Solve for the probability of waiting time

It is given that $x$ is p.d.f

$$\begin{gathered} P(0\le x\le 4)={\int }_0^{4}f\left(x\right)dx \\ ={\int }_0^4\frac{1}{5}dx \\ ={\left[\frac{x}{5}\right]}_0^4 \\ =\frac{4}{5}=0.8 \end{gathered}$$

Hence the probability of waiting time is $0.8$ and therefore option (B) is correct.