Cheyenne and Jacob are geocaching. They are currently hiking on a main trail at a bearing of N 45° E. They determine that the cache should be about 1.5 miles off the trail at a bearing of N 17° E.

If they want to hike to a point 3 miles further along the main trail once they have located the cache, they will hike an additional .

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.