Question

Determine whether the following statement is true or false: If our original population follows a normal distribution, then it is approximately normal.

a) True
b) False

Answer 1

a) True

If a population follows a normal distribution, then it is approximately normal. The terms "normal distribution" and "approximately normal" are often used interchangeably to describe a bell-shaped curve with certain statistical properties, such as symmetry and specific percentages of data falling within standard deviations from the mean.

Answer 2

The statement is true. If the original population follows a normal distribution, then the sampling distribution of the means will also be approximately normal.

Step-by-step explanation:

The statement is true. If the original population follows a normal distribution, then the sampling distribution of the means will also be approximately normal. This is known as the Central Limit Theorem. The Central Limit Theorem states that as the sample size increases, the sampling distribution of the means approaches a normal distribution, regardless of the shape of the original population distribution.