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QUIZ 3-4 - the top 3 of the fish population How much did...

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STAT 400 Spring 2011 Version D Name ANSWERS . Quiz 3 (10 points) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. The weight of fish in Lake Paradise follows a Normal Distribution with mean of 7.7 lbs and standard deviation of 2.5 lbs. a) (4) What proportion of fish are between 6 lbs and 10 lbs? P ( 6 < X < 10 ) = - < < - 5 . 2 7 . 7 10 Z 5 . 2 7 . 7 6 P = P ( – 0.68 < Z < 0.92 ) = Φ ( 0.92 ) Φ ( 0.68 ) = 0.8212 – 0.2483 = 0.5729 . b) (3) Mr. Statman boasts that he once caught a fish that was just big enough to be in
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Unformatted text preview: the top 3% of the fish population. How much did his fish weigh? Need x = ? such that P ( X > x ) = 0.03. P ( Z > z ) = 0.03. Φ ( z ) = 0.97. z = 1.88. x = μ + σ ⋅ z = 7.7 + 2.5 ⋅ 1.88 = 12.4 lbs . c) (3) If one catches a fish from the bottom 9% of the population, the fish must be returned to the lake. What is the weight of the smallest fish that one can keep? Need x = ? such that P ( X < x ) = 0.09. Φ ( z ) = 0.09. z = – 1.34. x = μ + σ ⋅ z = 7.7 + 2.5 ⋅ ( – 1.34 ) = 4.35 lbs ....
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