# L33 Psych 300 Chapter Notes - Chapter 6: Normal Distribution, Central Limit Theorem, Standard Deviation

by OC2558341

Department

Psychological & Brain Sci (Psychology)Course Code

L33 Psych 300Professor

NestojkoChapter

6This

**preview**shows half of the first page. to view the full**2 pages of the document.**Chapter 06: The Normal Curve, Standardization, and z

Scores

The Normal Curve - a specific bell-shaped curve that is unimodal, symmetric, and defined

mathematically

●The normal curve describes the distributions of many variables

●As the size of a sample approaches the size of the population, the distribution resembles

a normal curve (as long as the population is normally distributed)

Building Blocks of Inferential Statistics:

●The characteristics of the normal curve

●How to use the normal curve to standardize any variable by using a tool called the z

score

●The central limit theorem, which, coupled with a grasp of standardization, allows us to

make comparisons between means

Standardization, z

Scores, and the Normal Curve

●Standardization - a way to convert individual scores from different normal distributions

to a shared normal distribution with a known mean, standard deviation, and percentiles

●z

Score - the number of standard deviations a particular score is from the mean

○Like all statistical symbols, the z

is italicized

○If your score is 2 standard deviations above the mean, your z

score is 2.0, if your

score is 1.6 standard deviations below the mean, your z

score is -1.6

■If the mean is 70, the standard deviation is 10, and your score is an 80,

your z

score is 1.0

○The z

distribution always has a mean of zero (0) and a standard deviation of 1

●How do we calculate a z

score?

○Determine the distance of a particular person’s score (X) from the population

mean (u

) as part of the calculation (X - u

)

○Express this distance in terms of standard deviations by dividing by the

population standard deviation, o

●Transforming z

Scores into Raw Scores

○Multiply the z

score by the population standard deviation (o

)

○Add the population mean (u

) to this product to get the raw score

○Make sure not to forget the negative sign if your z

score is negative

●The z

distribution is a normal distribution of standardized scores (z scores), and the

standard normal distribution is a normal distribution of z scores

●Using z

Scores to Make Comparisons:

○You can compare how you did on one test with how your friend did on a different

test by finding your z

scores - how far above or below the mean you were. This

shows who did better with respect to their class’ scores.

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