STAT 206 THE NORMAL DISTRIBUTION CHPT 6

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Continuous variable

assume any value on continuum

Continuous prob distributions vary by shape

Normal distribution, uniform, and experimental

Uniform

symmetrical known as rectangular distribution. every value equal likely

exponential 

right skewed mean > median 

For normal distribution mean, median and mode are all

equal

For normal distribution the location is determined by

mean

For normal distribution spread is determined by 

standard deviation 

changing mu or the mean shifts the distribution

left or right

changing o or standard deviation

increases or decreases the spread

Know the formula for the normal probability density function 

e and pi in this are constants

Standard normalized distribution has a mean of and a standard deviation of _

0 and 1

Standardized normal distribution

z= x-u/o

Standardized normal distribution have values above the mean as ___ z scores and values below the mean as ___ z scores

pos and neg

Standardized normal probability function formula 

know it e and pi are also constants again 

Probability is measured as

area under curve

total area under the curve is__ and area is _

1, symmetric . so half above mean and half below

P < z

use table

P > x

1- table number

btwn the 2 values do larger - smaller

Empirical rule: u±1o covers

68.26 of x

Empirical rule: u±2o

95.44

Empirical rule: u±3o

covers 99.73

Given a normal prob find x value

x= u+Zo

To check for symmetry (construct charts or graphs)

small+ make boxplot. large = is histogram symmetrical

Compute descriptive summary measures 

is it approx 6o. is mean median and mode same

normal probability plot for data from a normal

distribution will be approximately

linear

left skewed prob plot

upper left slice of pizza crust shape

right skewed

bottom right of water melon shape