in the blank.

The

SISTESTINATIOR O PARISSAR with any distribution. the distribution of the samole means aproaches a normal distribution as the sample size increase:

The

tells us that for a population with any distribution, the distribution of the sample means approaches a normal distribution

as the sample size increases

Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of = 1.4 kg and a stand:

= 5.2 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 weight gain exceeds 30, the distribution of sample means is a normal distribution for any sample size.

◯ B. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size.

◯ C. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any 

◯ D. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size.

The scores of individual students on the American College Testing (ACT) Program Composite College Entrance Examination have a Normal distribution with mean 18.6 and standard deviation 6.0. At Northside High, 36 seniors take the test. Assume the scores at this school have the same distribution as national scores. 1. What is the standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students? A) 1.0 B) 3.1 C) 6.0 D) 18.6

The scores of individual students on the American College Testing (ACT) Program Composite College Entrance Examination have a Normal distribution with mean 18.6 and standard deviation 6.0. At Northside High, 36 seniors take the test. Assume the scores at this school have the same distribution as national scores. 2. What is the mean of the sampling distribution of the sample mean score for a random sample of 36 students? A) 1.0 B) 3.1 C) 6.0 D) 18.6