An eagle flying in the air over water drops an oyster from a height of 39 meters. The distance the oyster is from the ground as it falls can be represented by the function h(t) = −4.9t 2 + 39, where t is time measured in seconds. To catch the oyster as it falls, the eagle flies along a path represented by the function g(t) = −4t + 27.

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.