Chapter 6.3, Problem 95E

a.

To determine

To find: The mean of R and interpret it.

Explanation of Solution

Given:

From exercise 91,

Number of trials ( n ) = 20

Probability of success ( p ) = 0.30

Formula used:

The formula to compute the mean and standard deviation are:

  $\begin{array}{l}\text{Mean}\left(\mu \right)=n\times p\\ \text{Standard deviation}\left(\sigma \right)=\sqrt{n\times p\times \left(1-p\right)}\end{array}$

Calculation:

The mean of R can be calculated as:

  $\begin{array}{c}\mu =n\times p\\ =20\left(0.30\right)\\ =6\end{array}$

Thus, the mean is 6.

Interpretation:

The computed value of mean shows that on an average out of 20 , 6 passangers will obtain a red light.

b.

To determine

To find: The standard deviation of R and interpret it.

Explanation of Solution

Calculation:

The standard deviation of R can be calculated as:

  $\begin{array}{c}\sigma =\sqrt{n\times p\times \left(1-p\right)}\\ =\sqrt{20\left(0.30\right)\left(1-0.30\right)}\\ =2.049\end{array}$

Interpretation:

The total number of passengers that obtain a red light will vary by 2.049 passenger in comparison of mean of 6 passengers.