For each of the following situations, find an interval that contains (approximately or exactly) 99.73 percent of all the possible sample means. In which cases must we assume that the population is normally distributed? Why?

(a) = 10, = 2, n = 25. (Round your answers to 2 decimal places.)

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= [ , ]; (Click to select) assume normal population do not assume normal population

(b) = 500, = .5, n = 100. (Round your answers to 2 decimal places.)

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= [ , ]; (Click to select) do not assume normal population assume normal population

(c) = 3, = .1, n = 4. (Round your answers to 2 decimal places.)

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= [ , ]; (Click to select) assume normal population do not assume normal population

(d) = 100, = 1, n = 1,600. (Round your answers to 3 decimal places.)

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= [ , ]; (Click to select) do not assume normal population assume normal population