z-scores

Normal distribution 2 variations

1. Mean 2. Standard deviation

Standard deviation normal distribution

It has a mean of 0 and a standard deviation of 1

Standard deviation

The spread, like a bunch of 7’s have a spread of 0, whereas a bunch with higher numbers and lower numbers,hers have a bigger spread

Z- scores

How far a number is from the average, using standard deviation as the unit

Az_ score of zero

The number is exactly the average

A positive z- score

Above the average

The average is 70 , and the standard deviation is 10

A score of 80, is 1 standard deviation above the average

X

Raw score

μμ

The mean

σ

Standard deviation

Z - score formula

Your score minus the average take that number then divide that number by the standard deviation

I got a score of 54 on an exam. The class average was 48, with a standard deviation of 2. What is my z score?

Take 54 - 48, which is 6, then divide by 2

Z score area under the curve example: •We know that 68% of the data within a standard normal distribution lies within one standard deviation of the mean

68% =0.68

1-0.68 =0.32

Meaning O. 32 does not lie between the standard deviation of the mean

We know that this 32% is divvied up into two tails, with each tail having 16% each.