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Probability of the weight of a quarter

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Currently, quarters have weights that are normally distributed with a mean of 5.670 g and a standard deviation of 0.062 g. A vending machine is configured to accept only those quarters with weights between 5.550 g and 5.790 g.

a) If 280 different quarters are inserted into the vending machine, what is the expected number of rejected quarters?

b) If 280 different quarters are inserted into the vending machine, what is the probability that the mean of 280 quarters falls between the limits of 5.550 g and 5.790 g?

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