A manufacturing process has 54 customer orders to fill. Each order requires one component part that is purchased from a supplier. However, typically 7% of the components are identified as defective, and the components can be assumed to be independent. (a) If the manufacturer stocks 57 components, what is the probability that the 54 orders can be filled without reordering components? (b) Let X be the number of good (i.e., non-defective) components among the 57 in stock. Find the mean of X. (c) Find the variance of X [from part (b)].

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Problem 5: Please answer parts a, b, and c.

Problem #5: A manufacturing process has 54 customer orders to fill. Each order
requires one component part that is purchased from a supplier.
However, typically 7% of the components are identified as
defective, and the components can be assumed to be independent.
(a) If the manufacturer stocks 57 components, what is the
probability that the 54 orders can be filled without reordering
components?
(b) Let X be the number of good (i.e., non-defective) components
among the 57 in stock. Find the mean of X.
(c) Find the variance of X [from part (b)].
Transcribed Image Text:Problem #5: A manufacturing process has 54 customer orders to fill. Each order requires one component part that is purchased from a supplier. However, typically 7% of the components are identified as defective, and the components can be assumed to be independent. (a) If the manufacturer stocks 57 components, what is the probability that the 54 orders can be filled without reordering components? (b) Let X be the number of good (i.e., non-defective) components among the 57 in stock. Find the mean of X. (c) Find the variance of X [from part (b)].
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