The number of siblings an individual has varies from student to student. The distribution of the number of siblings is strongly skewed to the right. The central limit theorem says that:________

(a) as we look at more and more students, their mean number of siblings gets ever closer to the mean u for all students.

(b) the mean number of siblings for any number of students has a distribution of the same shape (strongly skewed) as the distribution for individual students.

(c) the mean number of siblings for any number of students has a distribution that is close to Normal.

(d) the mean number of siblings for a large number of students has a distribution of the same shape (strongly skewed) as the distribution for individual students.

(e) the mean number of siblings for a large number of students has a distribution that is close to Normal.

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

By the Central Limit Theorem

The sampling distributions with a large number of students(at least 30) will be approximately normal, so the correct answer is given by option e.