Q3: A soft-drink bot bottles of soft drink obtained from the filling and capping
ID: 3060247 • Letter: Q
Question
Q3: A soft-drink bot bottles of soft drink obtained from the filling and capping machines. The probability, based on past data that a bottle came from "machine 1" and was nonconforming is (0.01) and that a bottle came from "machine 2" and was nonconforming is (0.025). Half the bot “machine 1 ” and the other half are filled on "machine 2". (a) Give an example of a simple event. (b) Give an example of a joint event. 0Q3: A soft-drink botling company maintains records conceming the number of unacceptabl tling company maintains records concerning of unacceptable tles are filled on ) If a filled bottle of soft drink is selected at random, what is the probability that: 1) it is a nonconforming bottle? 2) it is filled on "machine 2"? 3) it is filled on "machine 1" and is a conforming bottle? 4) it is filled on "machine 2" and is a conforming bottle? 5) it is filled on "machine 1" or is a conforming bottle? (d) Sup pose that we know that a bottle is filled on "machine 1", what is the probability that it is nonconforming? ) Suppose that we know that the bottle is nonconforming. What is the probability that it was (e) filled on "machine 1"? (D Explain the difference between the answers to (d) and (e). (g) Complete the following table P(conforming) P(nonconforming) Machine P(Total) Machine Machine P(Total)Explanation / Answer
a)) Events with single outcome called simple events.
Here, {nonconforming}, {conforming}, {machine 1} and {machine 2} are the simple events.
b)) Events with two or more characteristics called joint events. Here, {machine 1, nonconforming}, {conforming}, { } and {machine 2} are the joint events.
c)) (1) P(nonconforming) = P(nonconforming from machine 1) + P(nonconforming from machine 1)
= 0.01 + 0.025 =0.035
(2) P(filled on machine 2) = ½. Because there are two machines available.
(3) P(filled on “Machine 1” and “conforming bottle”) = 1 - P(filled on “Machine 1” and “NON-conforming bottle”)
= 1 – 0.01
=0.99.
(4)) ) P(filled on “Machine 2” and “conforming bottle”) = 1 - P(filled on “Machine 2” and “NON-conforming bottle”)
= 1 – 0.025
= 0.975.
(5) P(filled on “Machine 1” OR “conforming bottle”) = P(filled on “Machine 1”) + P(“conforming bottle”) - P(filled on “Machine 1” and “conforming bottle”)
= 0.5 + (1-0.035) – (0.975)
=0.49.
(d)) P(nonconforming | machine 1) = P(nonconforming int. machine 1)/ P(filled on “Machine 1”)
= 0.01/0.5
=0.02
(e)) P(machine 1 | nonconforming) = P(nonconforming int. machine 1)/ P(nonconforming)
= 0.01/0.035
=0.28571429
(f)) difference: (d) – (e) = -0.26571
Machine P(conforming) P(nonconforming) P(total) Machine 1 0.01 0.5 Machine 2 0.025 0.5 P(Total) 1Related Questions
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