A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 1087 people age 15 or older, the mean amount of time spent eating or drinking per day is 1.33 hours with a standard deviation of 0.58 hour. Complete parts (a) through (d) below.
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(a) A histogram of time spent eating and drinking each day is skewed right. Use this result to explain why a large sample size is needed to construct a confidence interval for the mean time spent eating and drinking each day.
A. Since the distribution of time spent eating and drinking each day is highly skewed right, a large sample size is needed to minimize the margin of error to ensure only the peak of the sampling distribution is captured in the confidence interval.
B. Since the distribution of time spent eating and drinking each day is highly skewed right, a large sample size is needed to ensure that it contains at least $5 \%$ of the population
C. Since the distribution of time spent eating and drinking each day is highly skewed right, a large sample size is necessary to ensure that the distribution of the sample mean is approximately normal.
D. Since the distribution of time spent eating and drinking each day is highly skewed right a large sample size is needed to maximize the margin of error to ensure that both tails are accounted for in the confidence interval