In a certain process, steel bars are manufactured and subjected to a torsion test. Bars are...

In a certain process, steel bars are manufactured and subjected to a torsion test. Bars are considered acceptable if they support 15lb-ft. Currently the process produces bars that average 15.23 lb-ft with a variance of 0.04 lb-ft ^ 2.

a) What proportion of the bars will not be able to meet the specifications?

b) If we take a sample of 50 bars, how many are expected to fail the test?

c) If we want no more than 5% of the bars to fail the specification, where should we place the average?

d) If we select a bar at random and we know that it meets the specification, what is the probability that it is above 15.2?

e) If from a batch of a thousand bars, 20 are extracted to be tested and the batch is rejected if a failure occurs, what is the probability of rejecting the batch?

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