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Binomial Distribution
Emma doesn't study for the exam and decides to rely on luck to pass the test by guesswork. Suppose she is going to take a test with 12 multiple-choice questions. Each question has 4 possible answers, only one of which is correct.
(1) What is the probability that Emma gets 2 and fewer answer correct?
(2) Suppose passing this test will require 50% accuracy in the answer. What is the probability that Emma will fail this test?
(3) Suppose Emma is taking this test along with another 39 students. Unluckily, the whole class decided to pass this test by luck. Each question weights 1 point. The full mark is 12 points. What is the class mean mark? What is the class standard deviation mark?
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