Question

For the population of one town, the number of siblings is a random variable whose relative frequency histogram has a reverse J-shape. Let x-bar denote the mean number of siblings for a random sample of size 30. For samples of size 30, which of the following statements concerning the sampling distribution of the mean is true?

x-bar is normally distributed.
	The distribution of x-bar has a reverse J-shape.
	x-bar is approximately normally distributed.
	None of the above statements is true.

Answer 1

Since, according to the Central Limit Theorem,

The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large (usually n > 30).

Hence, the sampling distribution of the mean will be approximately normally distributed.

Hence, the correct answer is:

• x-bar is approximately normally distributed.