stats

a 100 question multiple guess test has 5 responses for each question. Let X represent the number of correct answers, find E(X)
the answer is n=100, p=.2, q=.8
then E(X)=20

why is p 0.2 though?

p is probability of success on one trial, specifically the probability of correctly guessing on a single question.  The test can be thought of as an experiment with 100 trials, each question being a trial, analogous to flipping a coin 100 times.

So, the probability of guessing the 1 correct answer from 5 choices is p = 1/5 = 0.2

The problem is doable with the formula involved with binomial probability, to find any E(x) you want.

-- I mean any P(x) you want, probablity of getting x questions correct by guessing.  E(x), or expected value, is the same as the mean of the binomial distrution involved, mean = n times p.

Hm nice some anons known distributions