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.
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!
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 ?
It is really important that you get both of my answers.
To calculate the mean and standard deviation of the number of questions answered correctly when guessing on all ten questions, we need to use the binomial distribution.
In this case, each question has four choices, so the probability of guessing a question correctly is 1/4 or 0.25.
Mean (μ):
To find the mean, we multiply the total number of questions (10) by the probability of guessing a question correctly (0.25):
μ = 10 * 0.25 = 2.5
So, on average, you would expect to answer 2.5 questions correctly when guessing on all ten questions.
Standard Deviation (σ):
To find the standard deviation, we use the formula:
σ = sqrt(n * p * (1 - p))
where:
- n is the total number of questions (10)
- p is the probability of guessing a question correctly (0.25)
σ = sqrt(10 * 0.25 * (1 - 0.25))
= sqrt(10 * 0.25 * 0.75)
= sqrt(0.1875)
≈ 0.433
So, the standard deviation for the number of questions answered correctly when guessing on all ten questions is approximately 0.433.
It seems you've made an error in your calculation. The mean and standard deviation you mentioned are not correct. Double-check your calculations using the correct formulas and values.
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