Answer:
(e) the mean number of siblings for a large number of students has a distribution that is close to Normal.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
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.