Problem #5: A manufacturing process has 53 customer orders to fill. Each order r

Question

Problem #5: A manufacturing process has 53 customer orders to fill. Each order requires one component part that is purchased from a supplier. However, typically 3% of the components are identified as defective, and the components can be assumed to be independent (a) If the manufacturer stocks 55 components, what is the probability that the 53 orders can be filled without reordering components? (b) Let Xbe the number of good (i.e., non-defective) components among the 55 in stock. Find the mean of X. (c) Find the variance of X [from part (b)]. Problem #5(a): Problem #5(b): Problem #5(c):

Explanation / Answer

a)

By binomial distribution

p(x) = nCx px (1-p)n-x

p(x <=2) = p(x=0) + P(x=1) +p(x=2)

= 55C0 0.030 * 0.9755 +  55C1 0.031 * 0.9754 +  55C2 0.032 * 0.9753

= 0.772

b)

p(non defective component) = 1- 0.03 = 0.97

Mean = np = 55 * 0.97 = 53.35

c)

Varicance = np(1-p) = 55*0.97*0.03 = 1.6005

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