A company has three machines E1, E2, and E3 for making IKO resistors. It has bee

Question

A company has three machines E1, E2, and E3 for making IKO resistors. It has been observed that 80% of resistors produced by El are within 500 of thenominal value. Machine E2 produces 90% of resistors within 500 of the nominal value. The percentage for machine E3 is 60%. Each hour, machine El produces 3000 resistors, E2 produces 4000 resistors, and Es produces 3000 resistors. 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 a resistor that is within 502 of the nominal value? (b) If one resistor is selected from the bin and was found within 50 of the nominal value, what is the probability that it came from machine E?

Explanation / Answer

proportion of resistors produced by machine E1;E2 and E3 are in ratio: 3000:4000:3000

hence proportion of E1; E2 and E3 are (3/10); (4/10); (3/10)

a)

P(resisor within 50ohm)=P(frm E1 and within 50ohm+frm E2 and within 50ohm+frm E3 and within 50ohm)

=(3/10)*0.8+(4/10)*0.90+(3/10)*0.60=0.78

b)

P(macine E3|within 50 ohm)=P(machine E3 and ithin 50 ohm)/P(within 50 ohm)=(3/10)*0.60/0.78=0.2308

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