Quiz 10 Answers.pdf - • You may(and should use the fact...

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You may (and should) use the fact that if X is an N ( μ, σ 2 ) random variable, then its cdf is given by Pr( X x ) = Φ x - μ σ . 1. Suppose the value of Acme Co. is a normal random variable with an average of $125 million dollars and a standard deviation of $50 million. Compute the following probabilities, leaving answers in terms of Φ: (a) Probability that Acme Co. is worth less than $125 million. Let X be the value of Acme Co. Then Pr( X 125 mil) = Φ 125 mil - 125 mil 50 mil = Φ(0) = 0 . 5 . (b) Probability that Acme Co. is worth between $127 and $135 million. Pr(127 X 135) = Φ 135 - 125 50 - Φ 127 - 125 50 = Φ(1 / 5) - Φ(1 / 25) 2. A class of 120 students (independently) take an exam. Let S 120 be the class average. If we assume prior to the exam that each student has an expected grade of 72 with a standard deviation of 12, use the Central Limit Theorem approximate the probability that S 120 is within 4 points of 72. Leave your answer in terms of Φ. We are given that the expected score is μ = 72 with standard deviation σ = 12. CLT tells us that the class average S 120
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