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Discrete Math Section 17.4
Recognize various types of distributions. Apply normal
distribution properties.
A normal distribution is a bell
shaped curve.
Properties of a normal distribution
1. About 68% of the data is within one standard deviation of the mean.
2. About 95% of the data is within two standard deviations of the mean.
3. About 99% of the data is within three standard deviations of the mean.
The standard normal distribution is the normal distribution
having a mean of zero and a standard deviation of one. Its
graph is called the standard normal curve.
The equation of the
standard normal curve is :
Shaded area = P(z) = proportion
of the data less than z.
The area under the curve is
one. The area under the
. curve to the left of a
number z is the proportion
of the data having standard
values less than z.
The value of P(z) is called a percentile. A percentile
indicates the percent of people who scored lower than
someone with a standard value of z.
See table on page 664
• Find P(-2.1)
• Find P(-.6)
• Find P(1.8)
ww.measuringusability.com/pcalcz.php
On a test the mean score was 75 and the standard
deviation was 8. Find the percent of students that
scored less than 87.
• To find percentiles (the percent
of the data less than the z score)
using normal distributions
•
• 1. menu
• 2. statistics
• 3. distributions
• 4. normal Cdf
• 5. lower bound = 0
• 6. upper bound = <the desired
z score>
• 7. μ = 0
• 8. ϭ = 1
In a reaction test the responses were normally distributed
with a mean of 12 seconds and a standard deviation of 2.5
seconds. Find the percent of test subjects whose reaction
times were between 5 and 8 seconds.
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To find the percent of the data between two
z scores using normal distributions
1. menu
2. statistics
3. distributions
4. normal Cdf
5. lower bound = <lower z score>
6. upper bound = <upper z score>
7. μ = 0
8. ϭ = 1
On a standardized test, the mean was 70 and the standard
deviation was 4. What score would you have to make in order
to score at the 90th percentile?
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To find the z score based on
the percentile (area under
curve)
1. menu
2. statistics
3. distributions
4. inverse Normal
5. Area = <percentile>
6. μ = 0
7. ϭ = 1
Assignment
• Page 667
• Problems 1,4,6,8,10,11,12,14,15