232 A highly stressed machine parts time to failure is norma

2.32 A highly stressed machine part\'s time to failure is normally distributed with 90% of the failures occurring between 200 and 270h of use (i.e., 5% below 200h and 5% above 270 h). a. Find the mean and standard deviation of time to failure. b. Determine the part\'s life if no more than 1 % replacement probability can be tolerated. c. Compute the probability that life time of the part exceeds 50 h of use, if the part has been operating for 200 h without failure.

Solution

Confidence interval at 90% is (200,270)

Mean = average of 200 and 270

=235

1.67sigma. = margin of error= 235-200

Hence sigma = 35/1.67 = 20.96

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b) if 99% confi level

then conf interval = (235+or -2.,58 sigma)

= (180.92, 289.08)

c) P(X>250) = P(Z>0.72) = 0.5-0.2642

= 0.2358