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QUIZ 3-5 - Need x such that P X> x = 0.10 Need z such...

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STAT 400 Spring 2011 Version E Name _________________________ 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 heights of adult males in Neverland are normally distributed with mean of 69 inches and standard deviation of 5 inches. a) (4) What proportion of adult males are between 5 feet (60 in) and 6 feet (72 in) tall ? P( 60 < X < 72 ) = - < - < 5 69 72 5 69 60 P Z = P( 1.80 < Z < 0.60 ) = area between 1.80 and 0.60 = Φ ( 0.60 ) – Φ ( 1.80 ) = 0.7257 – 0.0359 = 0.6898 . b) (3) How tall must a male be to be among the tallest 10% of the population?
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Unformatted text preview: Need x such that P( X > x ) = 0.10. Need z such that P( Z > z ) = 0.10. Φ ( z ) = 1 – 0.10 = 0.90. z = 1.28 . z x =-σ μ 28 . 1 5 69 =-x . x = 69 + 5 ⋅ 1.28 = 75.4 inches. A male must to be over 75.4 inches tall. c) (3) How "tall" must a male be to be among the shortest third of the population? Need x such that P( X < x ) = 0.3333. Need z such that P( Z < z ) = 0.3333. Φ ( z ) = 0.3333. z = – 0.43 . z x =-σ μ 43 . 5 69-=-x . x = 69 + 5 ⋅ ( – 0.43 ) = 66.85 inches. A male must to be under 66.85 inches "tall." If P( X < x ) = 0.33, then x = 69 + 5 ⋅ ( – 0.44 ) = 66.8 inches....
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