SOLUTION: I thought I understood the material presented in class but need assistance in completing/understanding problem: A student is to use random guessing on a multiple-choice test. O

Question 124182: I thought I understood the material presented in class but need assistance in completing/understanding problem:
A student is to use random guessing on a multiple-choice test. Out of five choices, there is only one correct answer for each question. Assume that you will observe the first three guesses by the student.
a. Find the sample space.
b. Construct a probability distribution for the number of questions answered correctly, x.
c. Draw the probability histogram
d. find the standard deviation of the number of questions answered correctly
e. find the expected value of the number of questions answered correctly
f. Give one-, two-, and three sigma interval
Appreciate your assistance in getting me started and understanding this better. This is a problem generated by the instructor and really can't find a good reference in the book we are using.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A student is to use random guessing on a multiple-choice test. Out of five choices, there is only one correct answer for each question. Assume that you will observe the first three guesses by the student.
a. Find the sample space.
ttt,ttf,tft,ftt,tff,ftf,fft,fff
---------------
b. Construct a probability distribution for the number of questions answered correctly, x.
P(x=3) = 1/8 ; P(x=2) = 3/8 ; P(x=1) = 3/8 ; P(x=0) = 1/8
-------------------------------------
c. Draw the probability histogram
I'll leave that to you.
---------------------------------------
d. find the standard deviation of the number of questions answered correctly
I'll leave that to you.
-----------------------------------------
e. find the expected value of the number of questions answered correctly
E(x)= 0*(1/8)+1(3/8)+2(3/8)+3(1/8) = 3/2
---------------------------
f. Give one-, two-, and three sigma interval
DISABLED_event_one= (3/2)+sigma=
two = (3/2)+2*sigma=
three = (3/2)+3*sigma=
===========================
Cheers,
Stan H.
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