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QUIZ 3-3 - Find the minimum GPA needed to be on the Honor...

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STAT 400 Spring 2011 Version C 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 2.64 and standard deviation 0.45. a) (3) What is the probability that a randomly selected student would have a GPA of at least 3.0? P ( X 3.0 ) = - 45 0 64 2 0 3 Z P . . . = P ( Z 0.80 ) = 1 – Φ ( z = 0.80 ) = 1 - 0.7881 = 0.2119 . 21.19% . b) (3) Students with GPA in the top 4% are placed on the Honor List.
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Unformatted text preview: Find the minimum GPA needed to be on the Honor List. Need x = ? such that P ( X > x ) = 0.04. Find z such that P ( Z > z ) = 0.04. Φ ( z ) = 1 – 0.04 = 0.96 . z = 1.75 . 75 1 45 64 2 . . . x =-. x = 3.4275 . c) (4) What is the probability that a randomly selected student would have a GPA between 2.1 and 3.0? P ( 2.1 < X < 3.0 ) = -< <-45 64 2 3 Z 45 64 2 1 2 P . . . . . . = P ( – 1.20 < Z < 0.80 ) = Φ ( 0.80 ) – Φ ( – 1.20 ) = 0.7881 – ( 1 – 0.8849 ) = 0.7881 – 0.1151 = 0.6730 . 67.30% ....
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