Alternate Sources of ruel Eighty six percent of Americans favor spending government money to develop alternative sources of fuel for automobilees. For a random sample of 130 Americans, find the mean, vanance, and standard deviation for the number who favor government spending for alternative fuels. Round your answers to three decimal places.

Fart:

Port 1 of 2
(a) Find the mean.

Mean:

Part:

Part 2 of 2
(b) Find the varnance and standard deviation.

Variance:
Standard deviation:

Ask by Wheeler Franklin. in the United States

Mar 22,2025

Question

Alternate Sources of ruel Eighty six percent of Americans favor spending government money to develop alternative sources of fuel for automobilees. For a random sample of 130 Americans, find the mean, vanance, and standard deviation for the number who favor government spending for alternative fuels. Round your answers to three decimal places.

Fart:

Port 1 of 2
(a) Find the mean.

Mean:

Part:

Part 2 of 2
(b) Find the varnance and standard deviation.

Variance:
Standard deviation:

Ask by Wheeler Franklin. in the United States

Mar 22,2025

UpStudy AI · Accepted Answer

**(a) Mean**

The mean number of Americans in the sample who favor government spending is given by  
$$
\mu = np\,,
$$  
where $$ n = 130 $$ and $$ p = 0.86 $$. Thus,  
$$
\mu = 130 \times 0.86 = 111.8\,.
$$

**(b) Variance and Standard Deviation**

The variance for a binomial distribution is given by  
$$
\sigma^2 = np(1-p)\,.
$$  
Substitute the values:  
$$
\sigma^2 = 130 \times 0.86 \times (1-0.86) = 130 \times 0.86 \times 0.14\,.
$$
First calculate $$ 0.86 \times 0.14 $$:
$$
0.86 \times 0.14 = 0.1204\,.
$$
Then,  
$$
\sigma^2 = 130 \times 0.1204 \approx 15.652\,.
$$

The standard deviation is the square root of the variance:  
$$
\sigma = \sqrt{\sigma^2} = \sqrt{15.652} \approx 3.956\,.
$$

Rounded to three decimal places:

- Variance: $$\sigma^2 \approx 15.652$$
- Standard Deviation: $$\sigma \approx 3.956$$
**(a) Mean** Mean: $$ \mu = 111.8 $$ **(b) Variance and Standard Deviation** Variance: $$ \sigma^{2} \approx 15.652 $$ Standard Deviation: $$ \sigma \approx 3.956 $$

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