Question 849621: Your accounting exam has 25 multiple choice questions. Since you studied for the exam, your chance of answering each question correctly is 0.60. What is the probability that you will answer at most 16 questions correctly?
Found 2 solutions by ewatrrr, swincher4391:
Answer by ewatrrr(24785)   (Show Source):
Answer by swincher4391(1107)  (Show Source):
You can put this solution on YOUR website! This is not fun to compute by hand (and by that I mean a calculator). Though you should still understand the theory.
The situation we have here is a binomial distribution. This is because there are only two situations. You either guess correctly or you guess incorrectly.
We'll define X as a binomial random variable with p = .60 and n = 25 where p is the probability of success per trial and n is the number of trials.
We want the P[X<=16]. We define P[X=x] as (n choose x) *  so when we say P[X<=16] we want the probability that x=0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16. That's 17 calculations all added together.
If we really wanted to calculate this by hand, the better way is to realize that if you take all probabilities added together, we get 1. So if we take 1 - (every other probability), we'd calculate much less. That is the probability that x = 17,18,19,20,21,22,23,24,25 and then subtracted from 1. At least we'd only calculate 9 probabilities as opposed to 17.
Here's where it is probably relevant to you. I'd imagine that you would be using your TI-83/84 to calculate this so invoke the binomcdf function. The way we use this is binomcdf(n,p,x). Remember I said that our n =25, p = .6, and x = 16.
:binomcdf(25,.6,16) = 
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