SOLUTION: It has been reported that 83% of federal government employees use e-mail. If a sample of 200 federal government employees is selected, find the mean, variance and standard deviatio

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Question 1195595: It has been reported that 83% of federal government employees use e-mail. If a sample of 200 federal government employees is selected, find the mean, variance and standard deviation of the number who use e-mail.
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

n = 200 = sample size
p = 0.83 = probability of success

mu = mean
mu = n*p
mu = 200*0.83
mu = 166

sigma^2 = variance
sigma^2 = n*p*(1-p)
sigma^2 = 200*0.83*(1-0.83)
sigma^2 = 28.22

sigma = standard deviation
sigma = sqrt(variance)
sigma = sqrt(28.22)
sigma = 5.312249994 which is approximate

Answers:
Mean = 166
Variance = 28.22
Standard Deviation = 5.312249994 (approximate)


For more information, check out the Binomial Probability Distribution.
The reason we have a binomial distribution is because either a person uses email or they don't. Also, any employee is independent of any other.