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131A_1_hw6 - μ-σ and μ D to those whose score is between...

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EE 131A Problem Set #6 Probability Wednesday, November 16, 2005 Instructor: Vwani Roychowdhury Due: Wednesday, November 23, 2005 1. Problem 3.46 2. Problem 3.47 3. If X is a normal random variable with parameters μ = 3 and σ 2 = 9, Fnd (a) P [2 < X < 5], (b) P [ X > 0], (c) P [ | X - 3 | > 6], (d) x 0 such that P [ | X - 3 | < x 0 ] = 0 . 682. 4. An examination is often regarded as being good (in the sense of determining a valid grade spread for those taking it) if the test scores of those taking the examination can be approximated by a normal density function. (In other words, a graph of the frequency of grade scores should have approximately the bell-shaped form of the normal density.) The instructor often uses the test scores to estimate the normal parameters μ and σ 2 and then assigns the letter grade A to those whose test score is greater than μ + σ , B to those whose score is between μ and μ + σ , C to those whose score is between
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Unformatted text preview: μ-σ and μ , D to those whose score is between μ-2 σ and μ-σ , and ± to those getting a score below μ-2 σ . Calculate the probability that a student will get A, B, C, D, ± respectively. 5. An expert witness in a paternity suit testiFes that the length (in days) of pregnancy (that is, the time from impregnation to the delivery of the child) is approximately normally distributed with parameters μ = 270 and σ 2 = 100. The defendant in the suit is able to prove that he was out of the country during a period that began 290 days before the birth of the child and ended 240 days before the birth. If the defendant was, in fact, the father of the child, what is the probability that the mother could have had the very long or very short pregnancy indicated by the testimony? 6. Problem 3.59 1...
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