Roger Has Read A Report That The Weights Of Adult Male Siberian Tigers Have A Distribution Which Is?

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• Merlyn (1 comments)
  8:20 pm on September 13th, 2009 1

  (a)
  P(X > 450) = 1 – P(X < 450) = 1 - P((X-390)/65 < (450-390)/65) = 1 - P(Z < 0.9231)
  (That is, convert to standard normal: Z = (X-mu)/sigma )
  From standard normal tables (using interpolation),
  P(Z < 0.9231) = 0.8220. So
  P(X > 450) = 1 – 0.8220 = 0.1780
  (b)
  The sample mean is approximately normally distributed with mean 390 and standard deviation 65/sqrt(4)
  Otherwise, the calculation proceeds exactly as for part (a)
  You should get 1 – 0.9675 = 0.0325

• texas123 (1 comments)
  8:33 pm on September 13th, 2009 2

  For any normal random variable X with mean ? and standard deviation ? , X ~ Normal( ? , ? ), (note that in most textbooks and literature the notation is with the variance, i.e., X ~ Normal( ? , ?² ). Most software denotes the normal with just the standard deviation.)
  You can translate into standard normal units by:
  Z = ( X – ? ) / ?
  Where Z ~ Normal( ? = 0, ? = 1). You can then use the standard normal cdf tables to get probabilities.
  If you are looking at the mean of a sample, then remember that for any sample with a large enough sample size the mean will be normally distributed. This is called the Central Limit Theorem.
  If a sample of size is is drawn from a population with mean ? and standard deviation ? then the sample average xBar is normally distributed
  with mean ? and standard deviation ? /?(n)
  An applet for finding the valueshttp://www-stat.stanford.edu/~naras/jsm/…
  calculatorhttp://stattrek.com/Tables/normal.aspx
  how to read the tableshttp://rlbroderson.tripod.com/statistics…
  In this question we have
  X ~ Normal( ?x = 390 , ?x² = 4225 )
  X ~ Normal( ?x = 390 , ?x = 65 )
  Find P( X > 450 )
  P( ( X – ? ) / ? > ( 450 – 390 ) / 65 )
  = P( Z > 0.923077 )
  = P( Z < -0.923077 )
  = 0.1779836
  In this question we have
  Xbar ~ Normal( ? = 390 , ?² = (65^2) / 4 )
  Xbar ~ Normal( ? = 390 , ?² = 1056.25 )
  Xbar ~ Normal( ? = 390 , ? = 32.5 )
  Find P( Xbar > 450 )
  P( ( Xbar – ? ) / ? > ( 450 – 390 ) / 32.5 )
  = P( Z > 1.846154 )
  = P( Z < -1.846154 )
  = 0.03243494

 

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