SOLUTION: Case 1: Company XYZ produces processed meat such as hotdog, ham and longganisa. To produce hotdog, a molding machine is being used. For the past month, the machine is producing h

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