## Question 661:

1

For this question we need to use the probabilities from the Binomial Distribution. There are published tables of binomial probabilities and you can compute them by hand. Another alternative is to use Excel's built in binomial probability function =BINOMDIST() which will save a lot of error-prone hand calculations.  We have a sample size of 10 (n=10) and expected probability of .25.

For the first part of the question, wed enter the values =BINOMDIST(6,10,0.25,FALSE) where the parameters are 6: the number of questions correctly chosen, 10: the total number of questions attempted, .25: the probability of guessing a correct answer and FALSE means NOT to add up all the values from 0 to 6.  Excel gives us the probability of 0.01622 (thats a 1.622 percent chance of getting exactly 6 right).

For part b, the only difference is we want the probability of getting 0,1,2,3,4,5 or 6 correct. So we need to add up all the probabilities. Fortunately excel lets us just change the last parameter to TRUE =BINOMDIST(6,10,0.25,TRUE), and we get the answer: .99649  (thats a 99.649 percent chance of getting at most 6 rightwhich makes sense b/c to get more than 6 right from guessing is very unlikely).

For the 3rd part, we need the probability of 6,7,8,9 or 10, which is at least 6 correct and means passing. So we change the formula a bit and add up the probability from 0 to 5. The formula is now =BINOMDIST(5,10,0.25,TRUE) and we get the probability of .98027. Were almost done. We need the probability of more than this amount, so we subtract it from 1 = 1-.98027 = .0197. So the probability of passing the quiz ( getting 6 or more correct is .0197 or 1.97%)