Question: A manufactured part is engineered to have a population mean diameter (µ) of 70 inches, with a population standard deviation (σ) of five inches. A sample of 100 parts is drawn from an assembly line.

For this problem, be sure to use the z-calculation that is for sample means, and includes the sample size:

Z = \[(\bar{x}\] - m)/(s/ \[\sqrt{n}\] ). It is important that you understand why you use this expression here. See the text starting on page 261.

a. What is the probability that a sample mean calculated from your sample of 100 parts will have a diameter between 69 and 71 inches?

b. What is the probability that a sample mean calculated from your sample of 100 parts will be less than 70.5 inches in diameter?

c. Why do I not need to state that the distribution of measures of diameter for individual manufactured parts is normal in order to do parts a. and b. of this problem? Please answer in a single sentence.

d. Is the normal distribution a “continuous” or a “discrete” distribution? In a single sentence, explain why?