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The weight of a dozen eggs. The weight of the eggs produced by a certain breed of hen is Normally distributed with a mean of

The weight of a dozen eggs. The weight of the eggs produced by a certain breed of hen is Normally distributed with a mean of 65 grams and a standard deviation of 5 grams. If cartons of such eggs can be considered a simple random sample (SRS) of size 12 from the population of all eggs:

a) What is the standard error for the sample mean of a dozen eggs?

b) What is the probability that the sample mean of the weight of a carton will be between 755 and 830 grams?

c) What is the probability that the sample mean of a carton will be below 744 grams?

d) Above what value do 2.5% of the sample means fall?

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