document.write( "Question 648065: Case 1: Company XYZ produces processed meat such as hotdog, ham and longganisa. To produce hotdog, a molding machine is
\n" ); document.write( "being used. For the past month, the machine is producing hotdogs with inconsistent weight. Thus, the manager wants his production
\n" ); document.write( "engineer to analyze the machine. A certain lot of hotdogs with 12 units was specially produced. 3 units were sampled by the quality
\n" ); document.write( "inspector. The said lot contains 5 defective units.
\n" ); document.write( "a. Write the probability distribution of the random variable X, which is the number of good units in the sample.
\n" ); document.write( "b. Find the expected value of the number of good units in the sample.
\n" ); document.write( "c. Find the probability that in the sample taken, there is no item that is defective.
\n" ); document.write( "d. Find the probability that at least two items are found defective in the sample taken
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Algebra.Com's Answer #406563 by stanbon(75887)\"\" \"About 
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Case 1: Company XYZ produces processed meat such as hotdog, ham and longganisa. To produce hotdog, a molding machine is
\n" ); document.write( "being used. For the past month, the machine is producing hotdogs with inconsistent weight. Thus, the manager wants his production
\n" ); document.write( "engineer to analyze the machine.
\n" ); document.write( "-------------------------------------
\n" ); document.write( " A certain lot of hotdogs with 12 units was specially produced. 3 units were sampled by the quality inspector. They said lot contains 5 defective units.
\n" ); document.write( "-------------------------------------
\n" ); document.write( "a. Write the probability distribution of the random variable X, which is the number of good units in the sample.
\n" ); document.write( "Binomial with n = 12 and P(defect) = 5/12 ; P(good) = 7/12
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\n" ); document.write( "b. Find the expected value of the number of good units in the sample.
\n" ); document.write( "E(x) = np = 12*(7/12) = 7
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\n" ); document.write( "c. Find the probability that in the sample taken, there is no item that is defective.
\n" ); document.write( "P(x = 0) = (7/12)^12 = 0.0015
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\n" ); document.write( "d. Find the probability that at least two items are found defective in the sample taken
\n" ); document.write( "P(2<= x <= 12) = 1 - P(0<= x <=1) = 1 - binomcdf(12,5/12,1) = 0.9851
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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