SOLUTION: Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of poss

Algebra ->  Probability-and-statistics -> SOLUTION: Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of poss      Log On


   

Question 1104256: Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of answers to different questions are independent. Jodi is a good student for whom p = 0.77.
How many questions must the test contain in order to reduce the standard deviation of Jodi's proportion of correct answers to half its value for a 100-item test?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of answers to different questions are independent. Jodi is a good student for whom p = 0.77.
How many questions must the test contain in order to reduce the standard deviation of Jodi's proportion of correct answers to half its value for a 100-item test?
----
Find original standard deviation::
mean = np*100*0.77 = 77
std = sqrt(npq) = sqrt(77*0.23) = 4.104
--------
New conditions. Find "n".
(4.104)/2 = sqrt(npq)
2.052 = sqrt(n*0.77*0.23)
4.211 = 0.1771n
n = 24 when rounded up
-------------
Cheers,
Stan H.
---------------