A production supervisor at a major chemical company wishes to determine whether a new catalyst, catalyst XA100, increases the mean hourly yield ofa chemical process beyond the current mean hourly yield, which is known to be roughly equal to, but no more than, 750 pounds per hour. To test the new catalyst, five trial runs using catalyst XAleO are made. Assuming that all factors affecting yields of the process have been held as constant as possible during the test runs, it is reasonable to regard the five yields obtained using the new catalyst as a random sample from the population of all possible yields that would be obtained by using the new catalyst. Furthermore, we will assume that this population is approximately normally distributed. Regard the sample of 5 trial runs for which s= 19.71 as a preliminary sample. Determine the number of trial runs of the chemical process needed to make us: (Round up your answers to the next whole number.) (a) 95 percent confident that 36 , the sample mean hourly yield, is within a margin of error of 8 pounds of the population mean hourly yield ,uwhen catalyst XA1OO is used. trial runs (b) 99 percent condent that 7c is within a margin of error of 5 pounds of u