The director of quality of a company manufacturing heavy fabrics is interested in studying the warpwise breaking strength of fabric. breaking strength is known to be approximately normally distributed. the following data represent the warpwise fabric breaking strengths (in pounds per square inch) for a random sample of 25 pieces:
196.5 198.1 192.1 200.1 203.2 202.9 207.3 201.7 207.5 207.7 195.5 198.4 192.3 189.9 196.1 197.9 202.4 189.9 198.1 204.7 205.3 189.5 202.1 210.2 196.9
(a) calculate a 99% confidence interval that estimates the average breaking strength for all such fabric pieces.
(b) calculate a 99% tolerance interval for the breaking strength that will include 95% of all the fabric pieces.