# Ex6 - THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 1306 INTRODUCTORY STATISTICS Sem 1 2008/2009 EXAMPLE CLASS 6 NORMAL DISTRIBUTION 1. Let Z be the standard normal random variable and let X be a normal random variable with mean 80 and standard deviation 10. Calculate the following probabilities: a) P(Z<-1.37) b) P(Z>-1.75) c) P(X>90) 2. For a particular reading comprehension test, the scores X are regarding as having a normal distribution with mean μ = 80 and variance 2 σ =16. Find the fraction of all scores on the reading comprehension test between 78 and 85.

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3. Let Z be the standard normal random variable and let X be a normal random variable with mean 80 and standard deviation 10. Find z and x for the following: a) P(0<Z<z)=0.379 b) P(|Z|<z)=0.95 c) P(Z >z)=0.9 d) P(X<x) = 0.95 4. A random variable X is known to follow a normal distribution with mean μ =62.4. Find the standard deviation of X if 20% of the area under the normal curve lies to the right of 79.2.
5. X~N(

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## This note was uploaded on 09/06/2010 for the course STAT STAT1306 taught by Professor Prof during the Fall '08 term at HKU.

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Ex6 - THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS...

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