# statistics

A multiple choice test has 20 questions with each having 4 possible answers with one correct. Assume a student randomly guesses the answer to every question.

1) What is the probability of getting exactly 9 correct answers?

2)What is the probability of getting less than 9 correct answers?

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1. prob of R(ight) = 4/20 = 1/5
prob of W(rong) = 4/5

1) to have exactly 9R and 11W
= C(20,9)((1/5)^9(4/5)^11
= ....

( I got .00722)

2) to get the prob of less than 9 you will have to do
prob(0R) + prob(1R) + prob(2R) + .. + prob(8R)

I will do prob(R4)
= C(20,4)(1/4)^4(4/5)^16 = .21819

Follow the same pattern for the other calculations

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2. a test consists of 25 multiple choice questions. Each has 5 possible answers, which only one is correct. If a student guesses on each question, find the following:
a) prob that he will guess all of them right
b)prob that he will guess at most 12 right
c) prob that he will guess at least 1 right
d) mean and stndrd. deviation of the number of correct answers
e)estimate the prob of the number of correct answers that will fall within the limits -----> miu +or- 2(stand.dev)

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3. Suppose a student takes a 20 question multiple-choice test and guesses at every answer. If there are exactly four choices on each question, what is the probability the student passes the test? (Assume passing means the student gets at least 60% of the questions correct.)

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4. 0999

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