The bottling process is known to have a standard deviation of 8 milliliters. Recently, you have noticed a significant number of bottles are overfilled and leaking. You hope to work with Joe to reduce the frequency of this occurrence. What must the target mean for the filling process be to ensure that bottles are overfilled less than 2 percent of the time?

Thompson and thompson is a steel bolts manufacturing company. their current steel bolts have a mean diameter of 127 millimeters, and a variance of 36. if a random sample of 35 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 0.5 millimeters? round your answer to four decimal places.