In the article "Drinking Glucose Improves Listening Span in Students Who Miss Breakfast" (Educational Research, Vol. 43, No. 2, pp. 201-207), authors N. Morris and P. Sarll explored the relationship between students who skip breakfast and their performance on a number of cognitive tasks. According to their findings, blood glucose levels in the morning, after a 9-hour fast, have a mean of 4.60 mmol/L with a standard deviation of 0.16 mmol/L.
a. Determine the sampling distribution of the sample mean for samples of size 60.
b. Repeat part (a) for samples of size 120.
c. Must you assume that the blood glucose levels are normally distributed to answer parts (a) and (b)? Explain your answer.