CEE3770_Sum09_HW4_solns

# CEE3770_Sum09_HW4_solns - CEE 3770 Summer 2009 Homework 4...

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CEE 3770 - Summer 2009 Homework 4 Solutions(due on 06/25) 1. Of 50 arrows shot at a target, 35 were hits. Determine 80% conﬁdence limits for the proba- bility of a hit. Hint: Use an approximation method. Solution: X = 35 / 50 = 0 . 7 and V ar ( X ) = p (1 - p ) /n = 0 . 7 · 0 . 3 / 50 = 0 . 0042. By CLT, X N (0 . 7 , 0 . 0042). 80% CI = X ± z 0 . 1 s X (1 - X ) n = 0 . 7 ± 1 . 28 0 . 042 = 0 . 7 ± 0 . 083 2. A Gallup Poll estimated the support among Americans for “right to die” laws. For the survey, 1528 adults were asked whether they favor voluntary withholding of life-support systems from the terminally ill. The results: 1238 Said yes. (a) Find a 99% conﬁdence interval for the percentage of all adult Americans who are in favor of “right to die” laws. Solution: X = 1238 / 1528 = 0 . 81 and V ar ( X ) = p (1 - p ) /n = 0 . 81 · 0 . 19 / 1528 = 0 . 00010072. By CLT, X N (0 . 81 , 0 . 00010072). 99%

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CEE3770_Sum09_HW4_solns - CEE 3770 Summer 2009 Homework 4...

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