A machine produces nails with the target mean length of 3 inches and historical standard deviation of 0.09 inches. A sample of 30 nails is selected, and it is found that the sample mean is 2.90 inches.
a) Find a 95% confidence interval of the mean length of all such nails produced by the machine.
b) Suppose we wanted the margin of error in estimating the true mean length of nails to be less than 0.02 with 95% confidence. What size of sample would be required?