SOLUTION: It has been observed that electrical connectors manufactured by Jolt Electrical Supply Company last an average of 18.2 months and follow a normal distribution with a standard devia

Question 428557: It has been observed that electrical connectors manufactured by Jolt Electrical Supply Company last an average of 18.2 months and follow a normal distribution with a standard deviation of 1.7 months. Jolt agrees to replace any connector that fails within 19 months. Out of 500 connectors sold, how many does Jolt expect to replace, on average?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
It has been observed that electrical connectors manufactured by Jolt Electrical Supply Company last an average of 18.2 months and follow a normal distribution with a standard deviation of 1.7 months. Jolt agrees to replace any connector that fails within 19 months. Out of 500 connectors sold, how many does Jolt expect to replace, on average?
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z(19) = (19-18.2)/1.7 = 0.4706
P(x< 19) = P(z< 0.4706) = 0.6810
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So 68.1% will last up to 19 mths.
So 0.3190 will fail in that period.
Jolt can expect to replace 0.319*500 = 160 units.
Cheers,
Stan H.
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