Question: A machine which manufactures a part for a car engine was observerd over a period of time before a random sample of 400 parts was selected from those produced by this machine. Out of 400 parts, 25 were defective. Find the sample mean of the proportion of defective parts.

(a) Referring to problem 1_3.6, find the sample standard deviation of the proportion of defective parts? Hint: Either a part is defective or it is not.

(b) Referring to problem 1_3.6, what is the probability that the sample proportion will lie within 0.01 of the true population of defective parts?