Normally distributed

Definition

A normally distributed variable follows a bell-shaped curve, symmetrical around its mean. This distribution is defined by its mean and standard deviation.

5 Must Know Facts For Your Next Test

1. The total area under the normal distribution curve is equal to 1.
2. Approximately 68% of data falls within one standard deviation of the mean.
3. 95% of data falls within two standard deviations of the mean.
4. The normal distribution is important for hypothesis testing because many test statistics are assumed to be normally distributed under the null hypothesis.
5. The Central Limit Theorem states that the sampling distribution of the sample mean approaches a normal distribution as the sample size grows.

Review Questions

• What percentage of data falls within two standard deviations from the mean in a normal distribution?
• Why is the normal distribution important in hypothesis testing?
• How does the Central Limit Theorem relate to normal distributions?

Related terms

Mean: The average value of a set of numbers, calculated by dividing the sum of all values by their count.

Standard Deviation: A measure of dispersion that indicates how spread out values are around the mean.

Central Limit Theorem: A statistical theory stating that, given a sufficiently large sample size, the sampling distribution of the sample mean will approximate a normal distribution regardless of the original population's distribution.