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Unformatted text preview: ) 1 , ( U in the usual manner, i.e. L , 3 , 2 , 1 ), ( ) ( ) ( = = k m X E k k ? Explain. (3) Question 2 [20] A farmer performs quality inspection on each batch of 144 eggs packed for market. Suppose that in a particular batch there are 15 substandard eggs. Of course, this is not known to the farmer. He selects, without replacement, a dozen eggs at random, and rejects the batch if he finds three or more substandard eggs in his sample. Let X denote the number of substandard eggs in his sample. (a) Find the density for X . Hint: Make a sketch! = ) ( x f (3) Sketch: (3) (b) Find ) ( X E and ) Var( X ) ( X E = (2) ) Var( X = (2) (c) Set up the calculation needed to find ) 3 ( ≥ X P ) 3 ( ≥ X P = (2) (d) Use the binomial tables to approximate ) 3 ( ≥ X P ) 3 ( ≥ X P = (3) (e) What is the probability that the farmer will reject this batch of eggs? (1) (f) Criticize the farmers decision rule: (4) END...
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 Fall '05
 n/a
 Statistics, Normal Distribution, Probability theory, probability density function, University of Missouri Department of Statistics, substandard eggs

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