2.5 Normal Distribution SWBAT calculate areas under a

standard normal curve in writing by converting between values and z-scores using a GCD or Table

Warm Up:

Pg 81 Exercise 84.

Why Normal Distributions?

It tells how variability in repeated measurements often behave

It tells you how variability in populations often behave

Its tells you how means computed from random sample behave

2.5 The Normal DistributionThe Standard Normal Distribution

Normal Distribution with a mean of 0 and SD of 1

Total area under the curve = 100% Standard Normal Distributions are

symmetrical Variable along the horizontal axis is

the z-score To find area or z-score, can use table

(pg 824-825) or calculator

Pg 85 D28

For the standard normal distribution: a) what is the median? b) what is the lower quartile? c) what z-score falls at the 95th

percentile? d) what is the IQR

2.5 The Normal DistributionThe Standard Normal Distribution

2.5 The Normal DistributionStandard Units Any normal distribution can be re-

centered and re-scaled to become a standard normal distribution.

Formula:

x meanz

SD

Calculator usage: NORMALCDF, INV NORM

2.5 The Normal DistributionSolving Problems

Always draw a picture! Worth pts Shade the part of the normal curve

you are trying to find If you are looking for a percentage,

you need a z-score (maybe even 2!) If you are looking for another value,

you will still need the z-score. Solve for the unknown.

2.5 The Normal DistributionCentral Intervals – See Handout

68% of the values lie with 1 SD of the mean

95% of the values lie within 2 SD of the mean

99.7% of the values lie within 3 SD of the mean

90% of the values lie within 1.645 SD of the mean

Pg 92 D31

Use Table A to verify that 99.7% of the values in a distribution lie within three standard deviations of the mean.

Problems

Practice for Normal Distribution WS Pg 92 P32-39

Homework:

Pg 93-94 E:59, 61, 63, 64, 67, 69, 71