Its the zoey question could you pl show your work and give the right answer

Ineed on 32 and 34! show work! correct gets brainliest! 50 points

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.

Which of the following is an example of conditional probability