2. A company has three machines A/, A2, and A3 making 1 k resistors. Resistors w
ID: 3324863 • Letter: 2
Question
2. A company has three machines A/, A2, and A3 making 1 k resistors. Resistors within 50 of the nominal value are considered acceptable. It has been observed that 70% of the resistors produced by Al, 80% by A, and 60% by A are acceptable. Each hour, machine A, A2, and A produce 3000, 2000, 5000 resistors, respectively. All of the resistors are mixed together at random in one bin and packed for shipment. a. What is the probability that the company ships an UNACCEPTABLE resistor? b. What is the probability that the unacceptable resistor comes from machine 3?Explanation / Answer
a) probability of unaccetable resistor =P(from A1 and unacceptable+from A2 and unacceptable+from A3 and unacceptable) =(3/10)*(1-0.7)+(2/10)*(1-0.8)+(5/10)*(1-0.6)=0.33
b) probability that unacceptable comes from machine 3 =P(from A3 and unacceptable)/P(unacceptable)
=(5/10)*(1-0.6)/0.33=0.6061
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