Normal Distribution

Emperical Rule is also know as what?

68-95-97.7 Rule

Process to finding area under curve using Z-Scores

Example: Your value(x)= 20 Mean(μ)=15 SD(σ)=3 Now Plug information into z score formula Z=(21-15)/3 = 2. Now you have your z sore value all you have to do is look that number up on the z table and there is your answer.

Assessing Normality

One can observe the shape of histograms, stemplots, and boxplots and see how well the data fit the 68-95-99.7 rules for normal distributions. A good method for assessing normality is to construct a normal probability plot.

Transforming Normal Distribution to Standard Normal Distributions

Use the Zscore Formula: Z= (x-μ)/σ x=Data Point μ=Mean σ=Standard Deviation

Invnorm Purpose?

Used to find a value or a z score if you know the area under the density curve to the left of the value.

Using Normalcdf

You need 4 numbers: Lower value, Upper value, Mean, and Standard deviation. LV=-e99, UV=e99, μ=0, σ=1 Example: normalcdf(-e99,e99,0,1)

68-95-97.7 Rule

-68% of values are within 1 standard deviation of the mean. -95% are within 2 standard deviations. -99.7% are within 3 standard deviations.

Process to convert a value to a Standard Score ("z-score")

-first subtract the mean, -then divide by the Standard Deviation

Z-Scores

Indicates by how many standard deviations a score is above or below the mean.

What Can the Z-Table also tell you?

It can tell you the percentile of how much data lies under a curve of the date.

Example to use Z-Table

Lets say you have z = 2.444. You look up on the left side of the table 2.4, then look across to the column under .04, where these two numbers cross gives the area under the graph of a normal distribution. In this case .9927 = area from the mean to the z score.

Two Pieces of data that specify a Distribution

Mean (μ) and Standard Deviation (σ)

Whats the Purpose of the TI-84 normalcdf?

Normalcdf is used if you are interested in finding the area under a curve.

Normal Distribution

a bell-shaped curve, describing the spread of a characteristic throughout a population

Z -Table

a table for the standard-normal curve giving z-scores in the margins and area under the curve to the left of the z-score