A 10 question test is all multiple choice. Each question has four choices. Determine the mean number of questions answered correctly as well as the standard deviation for the number of correct answers if someone were to guess on all ten questions.

Question

So far, I have that the probability of guessing each question right is 25%. I may have calculated wrong so far but I figured out the probability of getting one question right etc through 10 questions rights. I got the mean as 20.337 and the standard deviation being 217365.1244 which is WAY to high. Please help!

Answer 1

yes, p = .25
the mean better be ten/4 :)
which is 2.5

This is a binomial distribution

mean = n p = 10 * .25 = 2.5
(remarkable :)

sigma^2 = n p (1-p)
=10 (.25)(.75)
= 1.875

sigma = sqrt 1.875
= 1.37

Answer 2

let me do one point so you can see if an error

p of 2 right for example

P(10,2)= C(10,2) (.25)^2 (.75)^8
but
C(10,2) = 10![2! 8!]
= 10*9/2 = 45
so
P(10,2) = 45 (.0625)(.1)
= .282
does that agree ?

Answer 3

It is really important that you get both of my answers.