The skull breadths of a certain population of rodents follow a normal distribution with a standard deviation

Question:

The skull breadths of a certain population of rodents follow a normal with a standard deviation of 10 mm. Let be the mean skull breadth of a random sample of 64 individuals from this population, and let μbe the population mean skull breadth.
(a) Suppose μ = 50 mm. Find Pr{ is within ±2 mm of μ.}.
(b) Suppose μ = 100 mm. Find Pr{ is within ±2 mm of μ}.
(c) Suppose μ is unknown. Can you find Pr{is within ± 2 mm of μ} ? If so, do it. If not, explain why not.
Distribution
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