# QUIZ 3-2 - at least 3.0 P X ≥ 3.0 =-≥ 4 76 2 3 Z P = P Z ≥ 0.60 = 1 – Φ z = 0.60 = 1-0.7257 = 0.2743 27.43 c(4 What is the probability

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STAT 400 Spring 2011 Version B 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. Students’ GPA at Anytown College are approximately normally distributed with mean 2.76 and standard deviation 0.4. a) (3) Students with GPA in the top 3% are placed on the Honor List. Find the minimum GPA needed to be on the Honor List. Need x = ? such that P ( X > x ) = 0.03. Find z such that P ( Z > z ) = 0.03. Φ ( z ) = 1 – 0.03 = 0.97 . z = 1.88 . 88 1 4 0 76 2 . . . x = - . x = 3.512 . b) (3) What is the probability that a randomly selected student would have a GPA of

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Unformatted text preview: at least 3.0? P ( X ≥ 3.0 ) = -≥ 4 76 2 3 Z P . . . = P ( Z ≥ 0.60 ) = 1 – Φ ( z = 0.60 ) = 1 -0.7257 = 0.2743 . 27.43% . c) (4) What is the probability that a randomly selected student would have a GPA between 2.3 and 3.0? P ( 2.3 < X < 3.0 ) = -< <-4 76 2 3 Z 4 76 2 3 2 P . . . . . . = P ( – 1.15 < Z < 0.60 ) = Φ ( 0.60 ) – Φ ( – 1.15 ) = 0.7257 – ( 1 – 0.8749 ) = 0.7257 – 0.1251 = 0.6006 . 60.06% ....
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## This note was uploaded on 11/28/2011 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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QUIZ 3-2 - at least 3.0 P X ≥ 3.0 =-≥ 4 76 2 3 Z P = P Z ≥ 0.60 = 1 – Φ z = 0.60 = 1-0.7257 = 0.2743 27.43 c(4 What is the probability

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