Question

The waiting time for a bus at a certain bus stop has a uniform distribution over the interval from 0 to 25 minutes. (a) What is the probability that a person has to wait less than 6 minutes for the bus? (b) What is the probability that a person has to wait between 10 and 20 minutes for the bus?

Answer 1

Answer:

(a) The probability that a person has to wait less than 6 minutes for the bus is 0.24.

(b) The probability that a person has to wait between 10 and 20 minutes for the bus is 0.40.

Step-by-step explanation:

Let The random variable X be defined as the waiting time for a bus at a certain bus stop.

The random variable X follows a continuous Uniform distribution with parameters a = 0 and b = 25.

The probability density function of X is:

$f_{X}(x)=\left \{ {{\frac{1}{b-a};\ a$

(a)

Compute the probability that a person has to wait less than 6 minutes for the bus as follows:

$P(X$

                $=\frac{1}{25}\times \int\limits^{6}_{0}{1}\, dx$

                $=\frac{1}{25}\times [x]^{6}_{0}$

                $=\frac{1}{25}\times [6-0]$

                $=0.24$

Thus, the probability that a person has to wait less than 6 minutes for the bus is 0.24.

(b)

Compute the probability that a person has to wait between 10 and 20 minutes for the bus as follows:

$P10$

                          $=\frac{1}{25}\times \int\limits^{20}_{10}{1}\, dx$

                          $=\frac{1}{25}\times [x]^{20}_{10}$

                          $=\frac{1}{25}\times [20-10]$

                          $=0.40$

Thus, the probability that a person has to wait between 10 and 20 minutes for the bus is 0.40.