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. 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.
=====