Normal Distr
1
May 13, 2013
Oct 169:45 AM
Look at probabilities assigned to continuous variables.
Probability Density Functions
Normal Probability Density Function
The "Empirical Rule" 68, 95, 99.7
Standardizing variables
Using Standard Normal tables
Inverse Normal Calculations
Oct 169:52 AM
Look at probabilities assigned to continuous variables.
Probability of an exact value =
Probability of an interval =
Probability Density Functions
10
10 50
Think of probabilities as "Area Under a Curve"
Normal Distr
2
May 13, 2013
Oct 169:58 AM
105
Challenge!
What is the height of the probability density function?
What is the probability of a random value between 6 and 8?
Oct 13:57 PM
Along the xaxis is the number of standard deviations.
Standard Normal Distribtion
concave up
concave down
Inflection point
Normal Probability Density Function
Normal Distr
3
May 13, 2013
Oct 1610:16 AM
Texas A&M Stats Dept
Oct 1610:18 AM
Texas A&M Stats Dept
Normal Distr
4
May 13, 2013
Oct 1111:03 AM
Mean height amongst women is 66 inches with a standard deviation of 3 inches.
Emperical Rule 68 95 99.7% Rule
Oct 13:57 PM
Standard Normal Distribtion
68 95 99.7% RuleEmperical Rule
Assume that the leaf size of a maple tree has a mean of 17 cm and a standard deviation of 4 cm.
P(x > 17)=
P(x>21) =
P(13<x<21)=
N(17,4)
P(x<25)=
P(9 < x < 13)=
Practice Activity
Normal Distr
5
May 13, 2013
Oct 13:57 PM
Standard Normal Distribtion
68 95 99.7% RuleEmperical Rule
Assume that the leaf size of a maple tree has a mean of 17 cm and a standard deviation of 4 cm.
P(x > 17)=
P(x>21) =
P(13<x<21)=
N(17,4)
P(x<25)=
P(9 < x < 13)=
Practice Activity
Oct 1111:03 AM
Mean height amongst women is 66 inches with a standard deviation of 3 inches.
More practice??
Normal Distr
6
May 13, 2013
Oct 13:57 PM
Standard Normal Distribtion
The numbers along the xaxis for a Std. Normal Distr. are called?
P(z >0)
P(1< z < 2)
P(z > 1) P(z < 1.52)
Apr 37:36 AM
Normal Distribution Table
Finding Proportions using a Normal Distribution table.
P(1.96< z < 1.96)
Normal Distr
7
May 13, 2013
Oct 257:38 AM
Practice Using the table
Oct 257:38 AM
Normal Distr
8
May 13, 2013
Oct 257:38 AM
Oct 257:38 AM
Zvalue =
Example: Assume that the leaf size of a maple tree has a mean of 17 cm and a standard deviation of 4 cm.
P(x < 15.6) =
Standardizing variables
Normal Distr
9
May 13, 2013
Oct 257:38 AM
Oct 257:38 AM
Normal Distr
10
May 13, 2013
Oct 257:38 AM
Inverse Normal Calculations
Find the zvalue that corresponds to the area of the lower 80%.
Find the zvalue that corresponds to the area of the upper 10%.
Oct 257:38 AM
last one!
Normal Distr
11
May 13, 2013
Sep 301:20 PM
Normal Approximation to the Binomial
Suppose 1000 people have a 30% chance of having Opositive blood type.
What is the probability that 280 or less will have this blood type?
Calculate Mean and Std. Deviation
Sep 301:20 PM
Using a calculator!!
The Standard Normal Distribution
Normal Distr
12
May 13, 2013
Oct 257:44 AM
Generalizations...
Oct 257:40 AM
Normal Distr
13
May 13, 2013
Oct 257:40 AM
Oct 257:28 AM
