12­7 Normal Distributions 2011
February 25, 2011
Warm­Up
In a survey of 16 people, 1 person never locks
his car.
Find:
a) The sample proportion
12­7
Normal Distributions
b) The margin of error
c) The interval likely to contain the true population
Objectives: To use a normal distribution
and a standard normal curve
Feb 16­3:12 PM
What is a Normal Distribution?
A Normal Distribution shows data that varies randomly from the mean.
The pattern the data form is a bell­shaped curve....this is called a
Normal Curve.
Feb 16­3:25 PM
Standard Normal Curves
Characteristics:
• Centered on y­axis
• The mean is 0
• The standard deviation is 1
y
x
Feb 17­12:38 PM
Feb 17­12:57 PM
Example 1:
Every normal curve contains the same probability distribution
The jaw widths of a population of great white sharks are
normally distributed about a mean of 15.7 inches with a standard
deviation of 2.8 inches. Sketch a normal curve showing the jaw
width at 1, 2, and 3 standard deviations from the mean.
• 68% of the data fall within 1 standard deviations of the mean
What values are one standard deviation from the mean?
• 95% of the data fall within 2 standard deviations of the mean
• 100% of the data fall within 3 standard deviations of the mean
What percent of data is between 10.1 and 15.7?
Feb 17­1:07 PM
Feb 18­1:39 PM
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12­7 Normal Distributions 2011
February 25, 2011
Example 3:
Example 2:
The mean score on a quiz is 82 and the standard deviation
is 4. Estimate the percent of scores that were 90 or higher.
a. About how many students receive grades between one and two standard deviations above the mean?
Feb 17­1:17 PM
Example 4:
The mean wage for a company is $9.00 an
hour with a standard deviation of $1.50. If the
wages are approximately normally distributed,
determine the percent of workers getting paid
between $9.00 and $6.00 an hour.
Feb 17­1:28 PM
Review
Pg. 701 (2, 14, 18, 19­23, 27)
Pg. 704 (15­17, 20, 28­32 even)
HOMEWORK
Feb 18­1:57 PM
Feb 17­1:31 PM
Feb 18­7:58 AM
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