Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of $=1\mathrm{.}3kg$ and a standard deviation $0$ Complete parts $($a$)$ through $($c$)$ below.

a$.$ If $1$ male college student is randomly selected, find the probability that he gains between $0kg$ and $3kg$ during freshman year.

The probability is

$($Round to four decimal places as needed.$)$

b$.$ If $16$ male college students are randomly selected, find the probability that their mean weight gain during freshman year is between $0kg$ and $3kg.$

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 distribution is of individuals, not sample means, the distribution 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 original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.