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A certain population has a mean of 488 and a standard deviation of 31. Many samples of size 51 are randomly selected and the means calculated.

(a) What value would you expect to find for the mean of all these sample means? (Round your answer to the nearest whole number.)

(b) What value would you expect to find for the standard deviation of all these sample means? (Round your answer to two decimal places.)

(c) What shape would you expect the distribution of all these sample means to have?

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