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Recitation10Solutions

# Recitation10Solutions - 3 ¯ x ± 2 58 σ √ n = ± 58 3-2...

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Steven Weber Dept. of ECE Drexel University ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2008) Recitation 10 Solutions (Friday, June 6) Question 1. A CI is desired for the true average stray-load loss μ (Watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with σ = 3 . 0 . Please do the following: 1. Compute a 95% CI for μ when n = 25 and ¯ x = 58 . 3 . ¯ x ± 1 . 96 σ n = 58 . 3 - 1 . 96 3 . 0 25 , 58 . 3 + 1 . 96 3 . 0 25 = [57 . 124 , 59 . 476] . (1) 2. Compute a 95% CI for μ when n = 100 and ¯ x = 58 . 3 . ¯ x ± 1 . 96 σ n = 58 . 3 - 1 . 96 3 . 0 100 , 58 . 3 + 1 . 96 3 . 0 100 = [57 . 712 , 58 . 888] . (2) 3. Compute a 99% CI for μ when n = 100
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Unformatted text preview: 3 . ¯ x ± 2 . 58 σ √ n = ± 58 . 3-2 . 58 3 . √ 100 , 58 . 3 + 2 . 58 3 . √ 100 ² = [57 . 526 , 59 . 074] . (3) 4. Compute an 82% CI for μ when n = 100 and ¯ x = 58 . 3 . ¯ x ± 1 . 34 σ √ n = ± 58 . 3-1 . 34 3 . √ 100 , 58 . 3 + 1 . 34 3 . √ 100 ² = [57 . 898 , 58 . 702] . (4) 5. How large must n be if the width of the 99% interval for μ is to be 1 . ? n min = ³ 2 z α/ 2 σ w ´ 2 = µ 2 × 2 . 58 × 3 . 1 . ¶ 2 = 239 . 63 ⇒ n ≥ 240 . (5) www.ece.drexel.edu/faculty/sweber 1 June 6, 2008...
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