The temperature of a city steadily drops during the day until it is half of what it was at the beginning of the day. It then decreases by an additional 6.8ºF after the sun goes down. The temperature at the end of the day is −3.1°F. What was the temperature at the beginning of the day?

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.