Chapter 6.3, Problem 96E

a.

To determine

To find: The mean of T and interpret it.

Explanation of Solution

Given:

From exercise 92,

Number of trials ( n ) = 30

Probability of success ( p ) = 0.90

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 T can be calculated as:

  $\begin{array}{c}\mu =n\times p\\ =30\left(0.90\right)\\ =27\end{array}$

Thus, the mean is 6.

Interpretation:

The computed value of mean shows that on an average out of 30 , 24 passangers will have the mower starting.

b.

To determine

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

Explanation of Solution

Calculation:

The standard deviation of R can be calculated as:

  $\begin{array}{c}\sigma =\sqrt{n\times p\times \left(1-p\right)}\\ =\sqrt{30\left(0.90\right)\left(1-0.90\right)}\\ =1.6432\end{array}$

Interpretation:

The total number of times that mower starts will vary by 1.6432 times in comparison of mean of 27 times.