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The weight of the eggs produced by a certain breed of hen is Normally distributed with mean 65 grams & standard deviation 5 grams.

1) Calculate the probability that a randomly selected egg weights between 62.5 g and 68.75 g. Think of cartons of such eggs as SRSs of size 12 from the population of all eggs.
2) Calculate the probability that the mean weight of a carton falls between 62.5 g and 68.75 g.
3) Calculate the probability that the weight of the carton is more than 804 grams.
4) Did you need to know that the population distribution of egg weighs was Normal in order to complete parts 1 or 2 or 3? Justify.
5) Suppose you obtain a carton of eggs that is supposed to be from this type of hen, and only two of the eggs weigh between 62.5 g and 68.75 g. What would you conclude about whether the eggs came from this type of hen? Give appropriate statistical evidence to support your answer.

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