(a) The standard deviation of the sampling distribution is

= 0.04/11^0.5 = 0.0121.

The answer is

P( 1.77) = P(Z - 1.653) = 0.5 - 0.451 = 0.049

(b) No additional assumptions were required, because the probability distribution of the original distribution is normal. Thus, regardless of the sample size, the sampling distribution of the mean is normal.

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