Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of u = 1.1 kg and a standard deviation of = 5.1 kg. Complete parts (a) through (c) below.
a. If 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year.
The probability is ____. Round to four decimal places as needed.
b. If 4 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg.
The probability is ____. (Round to four decimal places as needed.)
c. Why can the normal distribution be used in part (b) even though the sample size does not exceed 30?
◯ A. Since the original population has a normal distribution. the distribution of sample means is a normal distribution for any sample size
◯ B. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size.
◯ C. Since the weight gain exceeds 30, the distribution of sample means is a normal distribution for any sample size.
◯ D. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size.