Intro to stat questions

the steps on how to do it would be great or just the answers.
1.About 9% of the population has a particular genetic mutation. 400 people are randomly selected.Find the standard deviation for the number of people with the genetic mutation in such groups of 400.

2.On a multiple choice test, each question has 5 possible answers.
(round your answers to 3 decimal places)
The probability of guessing any one question correctly is (.20)

Based on that probability, if the test had 15 questions, by just guessing one would "expect" to get 3 correct.

A.The probability of guessing fewer than 3 correct is_________
B.The probability of guessing more than 3 correct is _________.
i have no idea how to het 2 A and B. i do have a Calculator to do it on so if you know the steps but not the answers that would help a lot .

Ashley -

(1) Standard Deviation = sqrt (npq) = sqrt(400 x 0.09 x 0.91) = 5.72

(2A) P(X < 3) = P(X=0) + P(X=1) + P(X=2)

Now each of these probabilities is Binomial with n=15 and p = 0.20. For example,

P(X=2) = 15C2 (0.20)^2 (0.80)^13 = 0.2309

Now use the same technique on the other two probabilities:

P(X < 3) = P(X=0) + P(X=1) + P(X=2) = 0.0352 + 0.1319 + 0.2309 = 0.3980

P(X >3) = 1 - P(X less than or equal to 3) = 1 - [ P(X=0) + P(X=1) + P(X=2) + P(X=3) ]

You already know P(X=0) + P(X=1) + P(X=2) = 0.3980, so all you need is P(X=3) = 0.2502

P(X >3) = 1 - P(X less than or equal to 3) = 1 - 0.3980 - 0.2502 = 1 - 0.6482 = 0.3518

Hope that helped