Maine Corporation buys motors for electric fans from another company that guaran

Question

Maine Corporation buys motors for electric fans from another company that guarantees that at most 5% of its motors are defective and that it will replace all defective motors at no cost to Maine Corporation. The motors are recieved in large shipments. The quality control department at Maine Corporation randomly selects 20 motors from each shipment and inspects them for being good or defective. If this sample contains more than 2 defective motors, the entire shipment is rejected.

A) Find the probability that a given shipment of motors recieved by Maine Corporation will be accepted. Assume that 5% of all motors are defective.

B) Find the probability that a given shipment of motors recieved by Maine Corporation will be rejected.

Explanation / Answer

Let the 'X' be the event that Selected Motor is Defective

given p=5%=(5/100)

q=(100-5)%=95%=(95/100)

Total Number of motorsin the given sample=20

if more than 2 motors are defective then they are rejected

A) Find the probability that a given shipment of motors recieved by Maine Corporation will be accepted. Assume that 5% of all motors are defective.

Accepeted when number of defective motors<=2

P(x=0)+P(x=1)+P(x=2) (we know by binomial distribution P(x=r)=ncrprqn-r)

=20c0(5/100)0(95/100)20-0+20c1(5/100)1(95/100)20-1+20c2(5/100)2(95/100)20-2

=20c0(5/100)0(95/100)20+20c1(5/100)1(95/100)19+20c2(5/100)2(95/100)18

=(1).(1).(95/100)20+(20).(5/100).(95/100)19+(190).(5/100)2.(95/100)18

=0.9245(Approximately)

B) Find the probability that a given shipment of motors recieved by Maine Corporation will be rejected.

1-P(Accepted)=1-(0.9245)(From Solution A)

=0.0755

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