1. The inside diameter of a randomly selected piston ring is a random variable following normal distribution with mean value 12 cm and standard deviation 0.04 cm. (a) If is the sample mean diameter for a random sample of n = 16 rings, where is the sampling distribution of centered, and what is the standard deviation of the distribution? (b) Answer the questions posted in part (a) for a sample size of n =64 rings. (c) For which of the two random samples, the one of part (a) or the one of part (b), is more likely to be within 0.01 cm of 12 cm? Explain your reasoning

2. A sample of 58 data observations has a sample mean of 0.0328. If an experimenter wishes to use a "known" value =0.015 for the population standard deviation, construct an appropriate 95% confidence interval for the population mean .