Kendra is considering two different long–distance phone plans. phone plan a charges a $100 sign–up fee and 3 cents per minute. phone plan b does not charge a sign–up fee, but it charges 5 cents per minute.

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.