Normal distribution

Question 1

What does the normal distribution describe in statistics?

Answer 1

It describes how the values of a variable are distributed in a symmetrical, bell-shaped curve centered around the mean.

Question 2

What are the key parameters of the normal distribution?

Answer 2

Mean (μ) and standard deviation (σ). The mean determines the center, and the standard deviation determines the spread.

Question 3

What is the central limit theorem?

Answer 3

The central limit theorem states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population’s distribution.

Question 4

How much of a population is contained within 1 standard deviation in a normal distribution?

Answer 4

Approximately 68% of the population.

Question 5

How much of a population is contained within 2 standard deviations in a normal distribution?

Answer 5

Approximately 95% of the population.

Question 6

How much of a population is contained within 3 standard deviations in a normal distribution?

Answer 6

Approximately 99.7% of the population.

Question 7

What is the relationship between the sample mean and the population mean in a normal distribution?

Answer 7

The sample mean is an unbiased estimator of the population mean; they tend to converge as sample size increases.

Question 8

What type of distribution is described as having a constant probability across its range?

Answer 8

A uniform distribution.

Question 9

Why is the normal distribution important in statistical testing?

Answer 9

Because many statistical tests assume that the data follow a normal distribution, which simplifies inference and hypothesis testing.