A set of cards consists of 3 red cards and 7 black cards. You shuffle cards thoroughly and you turn cards over, one at a time, beginning with the top card. Let Y be the number of cards you turn over until you observe the first red card. The variable Y has which of the following probability distributions?

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A. 127 cm^2 b. 144.5 cm^2 c. 172 cm^2 d. 50 cm^2

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.