Distributions - Solution

Distributions - Solution - CE93 Engineering Data Analysis...

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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: 𝑋 ~ 𝑁 64.5,2.4 So: ? = 64.5 𝜎 = 2.4 a) P(X<63)? The z-statistic for X = 63 is: 𝑧 = 63 ? 𝜎 = 1.5 2.4 = 0.625 Thus: 𝑃 𝑋 < 63 = Φ 𝑧 = 1 Φ −𝑧 = 1 − Φ 0.625 = 1 0.7325 = 0.2675 b) P(X<70)? The z-statistic for X = 70 is: 𝑧 = 70 ? 𝜎 = 5.5 2.4 = 2.2917 Thus: 𝑃 𝑋 < 70 = Φ 𝑧 = 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: 𝑧 = 72 ? 𝜎 = 7.5 2.4 = 3.125 Thus: 𝑃 𝑋 < 72 = Φ 𝑧 = 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)
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e) 𝑃 𝑋 > 66 ? 𝑛 = 2 The z-statistic for 𝑋 > 66 is: 𝑧 = 66 ?
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