## Question 768:

1## Answer:

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For this question we can use the Binomial Probability mass function of pmf. First we see that the chance of getting a correct answer on any question is 20%, since there are 5 choices (1/5 = .20). Next we're told there are 25 total questions, and we need to find the probability of getting between 3 and 10 correct. So, we need to find the probability for each of these values, then add them all up to get our answer. This is best done using software. In excel we can use the formula =BINOMDIST() or on the TI-83 we can use the function binompmf. For the TI-83 we enter 25, .20, 3 to find the probability of getting exactly 3 correct out of 25, assuming the chance of getting any one correct is .20. See http://www.dacc.edu/~dyork/binomial_distribution.htm for more information on the TI-83 procedure.I've done the calculations in the attached excel file and when we add up all the values we get .89622, or there's a bit less than a 90% chance of getting between 3 and 10 correct.