Question

Bag check Refer to Exercise 91 .

a. Calculate and interpret the mean of R.

b. Calculate and interpret the standard deviation of R.

Short answer

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

(b)

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

Step-by-step solution

Part (a) Step 1: Given Information

Number of trials $\left(n\right)=20$

Probability of success $\left(p\right)=0.30$

Formula used:

The formula to compute the mean and standard deviation are:

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

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

Part (a) Step 1: Simplification

The mean of R can be calculated as:

$$\begin{gathered} \mu =n\times p \\ =20(0.30) \\ =6 \end{gathered}$$

Thus, the mean is 6 .

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

Part (b) Step 1: Given information

Number of trials $\left(n\right)=20$

Probability of success$\left(p\right)=0.30$

Part (b) Step 2: Calculation

The standard deviation of R can be calculated as:

$$\begin{gathered} \sigma =\sqrt{n\times p\times (1-p)} \\ =\sqrt{20(0.30)(1-0.30)} \\ =2.049 \end{gathered}$$

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