One step in the manufacture of a certain metal clamp involves the drilling of four holes. In a sample of 150 clamps, the average time needed to complete this step was 72 seconds and the standard deviation was 10 seconds.

a. Find a 95\% confidence interval for the mean time needed to complete this step.

b. Find a \(90 \%\) confidence interval for the mean time needed to complete this step.

c. Approximately how many clamps must be sampled so that a 95\% confidence interval specifies the mean to within \(\pm 1\) second?

d. Approximately how many clamps must be sampled so that a \(90 \%\) confidence interval specifies the mean to within \(\pm 1\) second?