Distributions - Solution

Distributions - Solution - CE93 – Engineering Data...

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Unformatted text preview: CE93 – Engineering Data Analysis Prof. Joan Walker – Spring 2011 Distributions – Practice Problems (First four problems are taken from the textbook “Probability and Statistics for engineers and Scientists, Fourth Edition” by Sheldon M. Ross): Problem 5.35 – Normal Distribution Let X = The height of the adult women. Then: ~ 64.5,2.4 ¡ So: ? = 64.5 = 2.4 a) P(X<63)? The z-statistic for X = 63 is: ∗ = 63 − ? = − 1.5 2.4 = − 0.625 Thus: < 63 ¡ = Φ ∗ ¡ = 1 − Φ − ∗ ¡ = 1 − Φ 0.625 ¡ = 1 − 0.7325 = 0.2675 b) P(X<70)? The z-statistic for X = 70 is: ∗ = 70 − ? = − 5.5 2.4 = 2.2917 Thus: < 70 ¡ = Φ ∗ ¡ = 0.9890 c) P(63 < X < 70) P(63 < X < 70) = P(X<70) – P(X<63) = 0.999 – 0.2675 = 0.7215 d) P(X<72)? The z-statistic for X = 72 is: ∗ = 72 − ? = − 7.5 2.4 = 3.125 Thus: < 72 ¡ = Φ ∗ ¡ = 0.999 (Note that if you are unable to look up the standard normal tables for z* = 3.1, this is because the table estimated this to be very close to 1) e)...
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This note was uploaded on 06/02/2011 for the course CIV ENG 93 taught by Professor Staff during the Spring '08 term at Berkeley.

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Distributions - Solution - CE93 – Engineering Data...

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