Paulina's family is going on a vacation. Their destination is 862 miles from home. The following events happen in order.

The family travels 348

miles and then stops at a lodge for the night.

The family travels another 144

miles and then stops at a rest stop.

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Please help me.

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.