The heights were recorded for a Simple Random Sample of 270 freshmen. The mean of this sample was ...

The heights were recorded for a Simple Random Sample of 270 freshmen.  The mean of this sample was 66.5 inches.  The heights are known to be Normally Distributed with a population standard deviation of 5.2 inches.  From the simple random sample of 270 freshmen heights:

i. Calculate the 97% Confidence Interval for the population mean height of a freshman.  Interpret the confidence interval.

ii. Calculate the 93% Confidence Interval for the population mean height of a freshman.  Interpret the confidence interval.  

iii. As you increase the level of confidence, how will this affect the precision (i.e., the width) of the interval?  (Note:  The smaller the interval, the more precise it is.)

iv. What sample size would you need for a 95% Confidence Interval to have a margin of error of no more than 0.5?