Lecture 3 - The Normal Distribution and Z Score

Question 1

What is important to know about the Mean, Median and Mode in a Normal Distribution?

Answer 1

They are the same

Question 2

What shape is a normal distribution on a density plot?

Answer 2

Symmetrical bell curve

Question 3

What can we calculate if we know the Mean and Standard Deviation for a normally distributed variable?

Answer 3

The proportion of scores above or below a certain value

Question 4

What is a Z-Score?

Answer 4

A standardised score for normal distribution. It shows how many standard deviations a score is away from the mean

Question 5

What is the formula for finding a z-score?

Answer 5

z = (x-μ) / σ

Key:
x = score
μ = mean
σ = standard deviation

Question 6

What is the formula for finding a score from a z-score?

Answer 6

x = μ + zσ

Key:
x = score
μ = mean
σ = standard deviation

Question 7

If a distribution is negatively skewed, what happens to the Mean, Median and Mode?

Answer 7

The mode will still be at the highest point of the curve, but the median and mode will be further towards the left, in the negative direction.

Question 8

If a distribution is positively skewed, what happens to the Mean, Median and Mode?

Answer 8

The mode will still be at the highest point of the curve, but the median and mean will be further towards the right, in the positive direction.

Question 9

What percentage of scores in a normal distribution are within 1 standard deviation of the mean?

Answer 9

68%

Question 10

What percentage of scores in a normal distribution are within 2 standard deviations of the mean?

Answer 10

95%

Question 11

What percentage of scores in a normal distribution are within 3 standard deviations of the mean?

Answer 11

99.7%