Eighty-five percent of Americans favor spending government money to develop alternative sources of fuel for automobiles. For a random sample of 120 Americans, find the mean, variance, and standard deviation for the number who favor government spending for alternative fuels

The data depict the binomial distribution because the outcome can be categorize into one of two categories that are American who favors and American who don't favor spending Govt. money to develop alternative sources of fuel for automobiles. The trial are independent and repeated 120 times. The probability of success is American who favors that is 85%.

The mean of binomial distribution is

mean=np

Here n=120 and p=0.85

Mean for the number who favor government spending for alternative fuels

mean=120*0.85=102

The variance of binomial distribution is

variance=npq

n=120, p=0.85 and q=1-p=1-0.85=0.15

The variance for the number who favor government spending for alternative fuels

Variance=120*0.85*0.15=15.3

The standard deviation for the number who favor government spending for alternative fuels can be found by taking the square root of variance

Standard deviation=√variance=√15.3

Rounding the value of standard deviation to two decimal places

Standard deviation=3.91

The mean, variance, and standard deviation for the number who favor government spending for alternative fuels are 102, 15.3 and 3.91 respectively.