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Recitation7Solutions

# Recitation7Solutions - students that will want to enroll...

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Steven Weber Dept. of ECE Drexel University ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2008) Recitation 7 (Friday, May 16) Question 1. Let X N ( μ, σ 2 ) denote a normal rv with mean μ and variance σ 2 , and let Z N (0 , 1) denote a standard normal. Use the table in the back of your book to answer the following questions. Please do the following. 1. Compute P ( Z 2 . 0) . P ( Z 2 . 0) = Φ(2 . 0) = 0 . 9772 . (1) 2. Let X N (3 , 9) . Compute P (0 X 3) . P (0 X 3) = P 0 - 3 3 X - 3 3 3 - 3 3 = P ( - 1 Z 0) = Φ(0) - Φ( - 1) = 0 . 5 - 0 . 1587 = 0 . 3413 . (2) 3. Find the 75% percentile for Z . Φ(0 . 67) = 0 . 7486 0 . 75 0 . 7517 = Φ(0 . 68) 0 . 67 z (0 . 75) 0 . 68 . (3) 4. Let X N (3 , 9) . Find the 75% percentile for X . x ( p ) = μ + σz ( p ) 3 + 3 × 0 . 68 = 5 . 04 . (4) 5. Let X N (3 , 9) . Find E [ X 2 ] . E [ X 2 ] = Var( X ) + E [ X ] 2 = 9 + 3 2 = 18 . (5) Question 2. When university administrators assign classrooms to classes they must estimate the number of
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Unformatted text preview: students that will want to enroll. Suppose the number of students wishing to enroll in a statistics class is normally distributed with mean 100 and a variance of 49 . Find the smallest classroom size suﬃcient to hold all interested students with probability at least 90% . Show all your steps and explain your solution procedure. P ( X ≤ c ) = P ± X-100 7 ≤ c-100 7 ² = P ± Z ≤ c-100 7 ² = Φ ± c-100 7 ² = 0 . 9 . (6) Observe Φ(1 . 28) ≈ . 9, hence c-100 7 = 1 . 28 ⇒ c = 100 + 7 × 1 . 28 = 100 + 8 . 96 ≈ 109 . (7) www.ece.drexel.edu/faculty/sweber 1 May 16, 2008...
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