Module 5: Normal Distributions

Question 1

What is a Normal Distribution?

Answer 1

A distribution based on a population of an infinite number of cases

Question 2

What are charcteristics of a Normal Distribution? (5)

Answer 2

Question 3

Why are normal distributions important?

Answer 3

• Some variables are believed to observe this distribution in the population
• Some statistical tests are based on this assumption (the variable is normally distributed)
• It allows us to calculate the percentage of the population above or below a given score

Question 4

What are the Differences between normal and sample (frequency) distributions? (4) (modality, symmetry, #)

Answer 4

Question 5

What is a Standard normal distribution?

Answer 5

It is a normal distribution measured in standard deviation units

Question 6

What are the charcteristics of the Standard normal distribution? (5)

Answer 6

Question 7

What is the 68, 95, 99.7% Rule?

Answer 7

68% of the population can be found
between -1 and 1 standard deviations

95% of the population can be found
between -2 and 2 standard deviations

99.7% of the population can be found
between -3 and 3 standard deviations

Question 8

What are the Differences between normal and standard normal distributions? (4) (unit, mean SD, values)

Answer 8

Question 9

Normal distribution
tranformed into
Standard normal distribution

Answer 9

Question 10

What does a z-score mean?

Answer 10

It is the distance from the mean (in standard deviations)

Z-score = 2 standard deviations
(i.e., is 2 standard deviations away [and above] of the mean)

Z-score = -1.5 standard deviations
(i.e., is 1.5 standard deviations away [and below] of the mean)

Question 11

Why is the Standard normal distribution important?

Answer 11

• Standardize units of measurement (comparisons are possible)
• Calculate distances from the mean
• Identify the relative position within a distribution
• Identify outliers
• Foundation of some statistical tests for hypothesis testing

Question 12

What do we need to transform Normal Distribution Scores to Standard Normal Deviation Z-Scores?

Answer 12

We will need the following:

• μ (population mean)
• σ (population standard deviation)
• X (individual scores)

Question 13

Z Score calculation Example:

Answer 13

Question 14

How do we transform Sample Distribution* Scores into Standardized Sample Distribution** Z-Scores?

* aka frequency distribution

• ** aka standardized distribution

Answer 14

We will need the following:

• 𝑋-bar (sample mean)
• s (sample standard deviation)
• X (individual scores)