Download The Standard Normal Distribution

2.5 Normal Distribution
SWBAT calculate areas under a
standard normal curve in writing by
converting between values and zscores 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 Distribution
The 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 Distribution
The Standard Normal Distribution
2.5 The Normal Distribution
Standard Units
Any normal distribution can be recentered and re-scaled to become a
standard normal distribution.
 Formula:

x  mean
z
SD

Calculator usage:
NORMALCDF,
 INV NORM

2.5 The Normal Distribution
Solving 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 Distribution
Central 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