The company producing the 1 pound and 10 pound bags of nuts and almonds from the
ID: 3251919 • Letter: T
Question
The company producing the 1 pound and 10 pound bags of nuts and almonds from the examination wants to concentrate on the 1 pound product. Remember that each bag could be classified in Grade A, Grade B, or Grade C, depending on the quality (A=Best, B= Medium, C= Low). The probability that a bag has a high percentage of bad nuts is 0.01, moderate percentage of bad nuts is 0.04, and low percentage of bad nuts is .95. Suppose that you select a sample of 3 bags, and the percentage of bad nuts in each of the bags is independent. Consider I and J the number of Grade A and Grade B bags out of the three, respectively. Estimate
a) P(i,j)
b) P(i)
c) E(I)
d) P(j|i=1)
e) E(J|I=1)
Explanation / Answer
a. P(I=i,J=j) = 0.95^i*0.0.4^j*0.01^(3-i-j), i + j<=3 and i,j>=0, i are of grade A, j of grade B and 3-i-j of grade C
b. P(I=i) = 0.95^i*0.05^(3-i)
c. E(I) = 0*0.05^3 + 1*0.95*0.05^2 + 2*0.95^2*0.05 + 3*0.95^2 = 2.800
d. P(J=j|i=1) = 0.95*.04^j.0.01^(2-j), as i=1, remaining 2 can be grade B or grade C