HW%234_f08_sol

# HW%234_f08_sol - CE 3102 Fall 2008 Homework #4 Due at 9:45...

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CE 3102 Fall 2008 Homework #4 Due at 9:45 AM, Thursday, October 16 2008 This is a team assignment. You may work together in teams of up to, but not exceeding, three people. Only one written submission is required from each team. However, every team member is responsible for knowing all of the material. 1. If the applied thickness, T, of a layer of bituminous asphalt paving material is Normally distributed with mean μ=4.0 inches and standard deviation σ =0.30 inches, find: P(T 3.70 inches) P(|T-μ| 0.30 inches) P(|T-μ| 0.30 inches| T 3.70 inches) (a) 8413 . 0 )) 0 . 1 ( 1 ( 1 ) 0 . 1 ( 1 ) 0 . 1 ( 1 .) 1 ( 3 . 0 0 . 4 7 . 3 3 . 0 0 . 4 ) 7 . 3 ( = = = = = = Z p Z P Z P Z P T P T P (b) 6827 . 0 ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 1 ( 3 . 0 3 . 0 3 . 0 3 . 0 3 . 0 3 . 0 ) 3 . 0 3 . 0 ( ) 3 . 0 | (| = = = = = = = Z P Z P Z P Z P Z P Z P T P T P T P σ μ (c) ) 7 . 3 ( ) 3 . 4 7 . 3 ( ) 7 . 3 ( ) 7 . 3 3 . 4 7 . 3 ( ) 7 . 3 ( )) 7 . 3 ( ) 3 . 3 . 0 (( ) 7 . 3 | 3 . 0 | (| = = = T P T P T P T T P T T T T P T T P Since 6827 . 0 ) 1 1 ( 3 . 0 4 3 . 4 3 . 0 4 3 . 0 4 7 . 3 ) 3 . 4 7 . 3 ( = = = Z P T P T P 8115 . 0 8413 . 0 6827 . 0 ) 7 . 3 | 3 . 0 | (| = = T T P

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2. 3. A random variable X=ln(Y) has a normal distribution, with a mean of 5.0 and a standard deviation of 1.0. Find the mean, variance, standard deviation, median and mode of the random variable Y. (Extra credit: find the coefficient of skewness for X.) Since X=ln(Y) has a normal distribution, Y has a lognormal distribution, and properties of the lognormal distribution are given on pp. 138-141 of the text.
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HW%234_f08_sol - CE 3102 Fall 2008 Homework #4 Due at 9:45...

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