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1. A student is taking a multiple-choice exam in which each question has four choices. Assume that the student has no knowledge of the correct answers to any of the questions. She has decided on a strategy in which she will place four balls (marked A, B, C, and D) into a box.
She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There are five multiple-choice questions on the exam. What is the probability that she will get a. at most four questions correct?
b. all questions correct?
c. one or two questions correct
2. Given the normally distributed variable X with mean 18 and standard deviation 2.5, find
(a) P(X > 17);
(b) the value of k such that P(X<k)=0.1814;
(c) P(15 <X< 19).
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