I have two questions that I need help solving:

It has been reported that 83% of federal government employees use email. If a sample of 200 federal government employees is selected, find the mean, variance, and standard deviation of the number who use email.

In a survey, 63% of Americans said they own an answering machine. If 14 Americans are selected at random, find the probability that exactly 9 own an answering machine.

If anyone can help that would be great, Thanks!

1. In your first problem,

n = 200
p = 0.83
q = 1-0.83 = 0.17

where n is the sample size,
p the probability of getting an employee using email.
and q the probability of getting an employee not using email.

Now,

Mean = np

Variance = npq

Standard\ Deviation = \sqrt{Variance} = \sqrt{npq}

Can you find the answers now? :)

2. Here, n = 14, p = 0.63, q = 1 - 0.63 = 0.37

You can use the binomial distribution for this one.

Let X be the event that an American own an answering machine.

X ~ B(14, 0.63)

Then, we know that:

P(X = x) =\ ^nC_x(p)^x(q)^{n-x}

It follows that;

P(X = 7) =\ ^{14}C_7(0.63)^7(0.37)^{14-7}

It's nearly done now.

Post your answers! :)