Question

American energy review reported that 27% of american households burn wood. if a random sample of 500 american households is selected find the mean, variance, and standard deviation of the number of households that burn wood.

Answer 1

This is binomial distribution problem. 
We are given that:

n = sample size = 500

p = proportion which burns wood = 0.27,

q = proportion which does not burn wood = 1-p = 0.73 

A. Mean is calculated as:

Mean = n*p

Mean = 500 * 0.27

Mean = 135 

B. Variance is calculated as:

Variance = n*p*q

Variance = 500*0.27*0.73

Variance = 98.55 

C. Standard deviation is calculated as:

Standard deviation = sqrt(variance)

Standard deviation = sqrt(98.55)

Standard deviation = 9.93