Question

Easy-start mower Refer to Exercise 92 .

a. Calculate and interpret the mean of T.

b. Calculate and interpret the standard deviation of T.

Short answer

(a)The computed value of mean shows that on an average out of $30,24$ passengers will have the mower starting.

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

Step-by-step solution

Part (a) Step 1: Given Information.

Given,

Number of trials $\left(n\right)=30$

Probability of success $\left(p\right)=0.90$

Formula used:

The mean and standard deviation are calculated using the following formula:

Mean $\left(\mu \right)=n\times p$

Standard deviation $\left(\sigma \right)=\sqrt{n\times p\times (1-p)}$

Part (a) Step 2: Simplification

The mean of T can be calculated as:

$$\begin{gathered} \mu =n\times p \\ =30(0.90) \\ =27 \end{gathered}$$

Thus, the mean is $6$ .

Interpretation:

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

Part (b) Step 1: Given information

Number of trials is $30$

Probability of success is $0.90$

Part (b) Step 2: Simplification

The standard deviation of $R$ can be calculated as:

$$\begin{gathered} \sigma =\sqrt{n\times p\times (1-p)} \\ =\sqrt{30(0.90)(1-0.90)} \\ =1.6432 \end{gathered}$$

In comparison to the mean of $27$ times, the total number of times the mower starts will vary by $1.6432$ times.