the normal distribution

Question 1

what are characteristics of a normal distribution?

Answer 1

a normal distribution has the same mean, mode and median. it is symmetrical about the mean. the graph of a normal distribution is called a ‘bell curve’

Question 2

what is the 68-95-99.7 rule?

Answer 2

for a normal distribution, approximately:
* 68% of data lie within one standard deviation of the mean
* 95% of data lie within two standard deviations of the mean
* 99.7% of data lie within three standard deviations of the mean
* 50% of data will lie above the mean and 50% of data will lie below the mean

Question 3

what is a z-score?

Answer 3

z-score is the number of standard deviations the score is from the mean

Question 4

what is the formula for z-scores?

Answer 4

z = x - μ
——-
s
where z - z-score
x - score
μ - mean of a set of scores
s - standard deviation

Question 5

what percentage of scores lie between each z-score on a normal distribution?

Answer 5

-4/-3 = 0.15%
-3/-2 = 2.35%
-2/-1 = 13.5%
-1/0 = 34%
0/1 = 34%
1/2 = 13.5%
2/3 = 2.35%
3/4 = 0.15%