Wires manufactured for a certain computer system are specified to have a resista

Question

Wires manufactured for a certain computer system are specified to have a resistance of between 0.12 and 0.14 ohm. The actual measured resistances of the wires produced by Company A have a normal probability distribution with a mean of 0.13 ohm and a standard deviation of 0.005 ohm. a) What is the probability that a randomly selected wire from Company A's production lot will meet the specifications? b) If four such wires are used in a single system and all are selected from Company A, what is the probability that all four will meet the specification? Company B also produces wires used in the computer system. The actual measured resistances of the wires produced by Company B have a normal probability distribution with a mean of 0.136 ohm and a standard deviation of 0.003 ohm. c) What is the probability that a randomly selected wire from Company B's production lot will meet the specifications? d) If four such wires are used in a single system and all are selected from Company B, what is the probability that all four will meet the specification? e) The computer firm orders 70% of the wires used in its systems from Company A and 30% from Company B. Suppose that all four wires placed in any one computer system are all from the same company and that the computer system will fail testing if any one of the four wires does not meet specifications. A computer system is selected at random and tested. It meets specifications. What the probability that Company A's wires were used in it?

Explanation / Answer

probabilty that company A's wire meet specification =P(0.12<X<0.14)=0.9545

and company B's wire meet specification =0.9088

e)hence probabilty that all 4 are from same company and meet specification s =(0.7*0.9545)4+(0.3*0.9088)4

hence probabilty that company A's wire used in it given all four from same company and meets specification

=(0.7*0.9545)4 /((0.7*0.9545)4+(0.3*0.9088)4) =0.9730

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