Manufacturing
a manufacturer's total cost is c(q) = 0.1q ^ 3 - 0.5q ^ 2 + 500q + 200 dollars when q thousand units are produced . currently , 4,000 units (q = 4) are being produced and the manufacturer is planning to increase the level of production to 4,100 . use marginal analysis to estimate how this change will affect total cost .

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.