Question

Use the following information to answer the next three exercises.

The Sky Train from the terminal to the rental–car and long–term parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution.

79. What is the average waiting time (in minutes)?

a. zero

b. two

c. three

d. four

Short answer

The average waiting time is (d)$4$minutes

Step-by-step solution

Defining Mean of uniform distribution.

Uniform distribution is a probability distribution that asserts that the outcomes for a discrete set of data have the same probability.

The Mean of the uniform distribution $U(a,b):\mu =\frac{(a+b)}{2}$.

Finding average waiting time

According to provided information, the random variable $X$for arrival of sky train is following uniform distribution such that:

$X~U(0,8)$ where$a=0,b=8$

And, it is known that mean of uniform distribution is:

$\mu =\frac{a+b}{2}$

So, average waiting time in minutes will be:

role="math" localid="1648185825397" $$\begin{gathered} \mu =\frac{0+8}{2} \\ =\frac{8}{2} \\ =4 \end{gathered}$$

Therefore, it can be said that option (d) is correct