1.The diameter of cylindrical shaft door hinge is normally distributed with a population mean of 12.8 mm and standard deviation of 3.35mm. The specifications on the shaft are 13 0.15 mm. What proportion of shafts conforms to the specification?

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2.The substance weight of a type of paper follows a normal distribution with a mean of 40 pounds per square inch and standard deviation of 3 pounds inch. What is the probability that the substance weight of a sample is greater than 45 pounds per square inch?

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3.If the specifications in Problem 2 require the substance weight to exceed 37 pounds per square inch, what portion of the sample is rejected?

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4.Consider a normal population with the mean = 86 and standard deviation = 10. If a random sample of size 58 is selected what is the probability that the sample mean x will fail between 84.5 and 88.2?

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5.The average life of industrial equipment that produces a certain product is 12 years, with a standard deviation of 1.7 years. If the average life of this equipment follows a normal distribution, find the value of x to the right of which 12% of the means computed from random samples of size 15 would fail.

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