It has been found that the time to failure in hours of a spr

It has been found that the time to failure (in hours) of a sprocket in a particular mechanical system is satisfactorily modeled as a Weibull random variable with shape parameter = 2 and scale parameter = 4000 hours. a) Determine the mean time until failure (in hours) for this population of sprockets. b) Determine the probability that the time until a sprocket from this population fails is at least 4000 hours. c) What lifetime (time to failure in hours) is exceeded by exactly half of all sprockets in this population? d) Complete the simulation of sprocket lifetimes below. Note that the random numbers in the middle column are draw from a continuous uniform distribution on the range (0,1), and = 2 and = 4000 hours. Sprocket Random Number Lifetime (hours) 1 .50 3330.22 2 .63 3988.49 3 .79 4997.04 4 .72 4513.03 5 .96 7176.49 6 .67 4211.72 7 .46 3139.90 8 .45 9 .29 10 .71 Sample mean = e) Based on the sample mean of the simulated lifetimes, how accurate is the simulation.

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