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.

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