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NASA needs astronauts to be between 62 and 75 inches. The average height for an American male is 70 inches with a standard deviation of 3 inches. The average height for an American female is 64.5 inches with a standard deviation of 2.5 inches. Heights are normally distributed. I take a sample of 32 American children. What is the probability that the mean height of these kids when they grow up will be in the acceptable range to become an astronaut? Compute the probability AND explain how you got it (which includes but may not be limited to saying what you typed into the calculator).

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