Sampling distribution of sample sample mean from normal.

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  the sampling distribution of the mean approaches a normal distribution with a mean (¦Ì) and a variance ¦Ò?N as N, the sample size, increases (http://davidmlane.com/hyperstat/sampling_dist.html).

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  Since the sample size is large, the sampling distribution of is a normal distribution with a mean of 0.555 and a standard deviation of c.

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  According to the central limit theorem, if the population is not normal but "sufficiently well behaved", the sampling distribution of the sample mean will still be approximately normal provided the sample size is sufficiently large.

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  The distribution of these means is the "sampling distribution of the sample mean" (for the given sample size). This distribution will be normal since the population was normal.