Protein shakes can act as a protein supplement such as for athletes that undergo rigorous strength training. Suppose the protein content of packets of a particular brand of protein shakes has population mean 20g and population standard deviation 0.9g. Assume that the protein content of packets follows very approximately a Normal distribution.

a) What proportion of packets will have a protein content of less than 19.5g?

b) What proportion of packets will have a protein content between 19g and 21g?

c) Now suppose a simple random sample of 12 packets is taken. What is the probability that the average protein content of this sample is above 20.2g?

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