UESTION 4 A manufacturing process has 120 customer orders to fill. Each order re
ID: 3207281 • Letter: U
Question
UESTION 4 A manufacturing process has 120 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 122 components, what is the probability that the 120 orders can be filled without reordering components?
b) If the manufacturer stocks 125 components, what is the probability that the 120 orders can be filled without reordering components?
Please explain! I am using a TI-84 Plus calculator.
Explanation / Answer
a)probability that the 120 orders can be filled without reordering components If the manufacturer stocks 122 components = P(no of non defective components =120)+P(no of non defective components =121)+P(no of non defective components =122) = 122C120*(0.97)120(0.03)2+122C121*(0.97)121(0.03)1+122C122*(0.97)122 = 0.2879
b)probability that the 120 orders can be filled without reordering components If the manufacturer stocks 125 components
= 125C120*(0.97)120(0.03)5+125C121*(0.97)121(0.03)4+125C122*(0.97)122(0.03)3+125C123*(0.97)123(0.03)2+125C124*(0.97)124(0.03)1+(0.97)125 = 0.825
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