Download Lesson 2.3A - Coweta County Schools

Significance of Experimental Results
• How do we use tables to estimate
areas under normal curves?
•How do we recognize data sets that
are not normal?
Holt McDougal Algebra 2
Significance of Experimental Results
Standard Deviation of a Data Set
A normal distribution with mean x and standard deviation
s has these properties:
•
1
The total area under the related normal curve is ____.
•
68 of the area lies within 1 standard deviation of the mean.
About ___%
•
95 of the area lies within 2 standard deviation of the mean.
About ___%
•
99.7
About _____%
of the area lies within 3 standard deviation of the
mean.
34%
68%
95%
99.7%
34%
13.5%
2.35%
13.5%
2.35%
0.15%
– 2s
–s
+ 3s
– 3s
+ 2s
+ 3s
+s
+ 2s
–s
+s
– 2s
x
x
x
x
x
x
Holt McDougal Algebra 2
x
x
x
x
x
x
x
x
– 3s
0.15%
+ 2s
+ 3s
–s
+s
– 2s
x
x
x
Holt McDougal Algebra 2
x
x
a. Px  x  x  2s 
0.34  0.135  0.475
b. Px  3s  x  x  s 
0.0235  0.135  0.1585
c. Px  s  x  x  3s 
0.34  0.34  0.135  0.0235  0.8385
d. Px  x  s 
0.50  0.34  0.84
x
x
Find a normal probability
1. A normal distribution has a
mean x and standard deviation
s. For a randomly selected xvalue from the distribution, find
– 3s
Significance of Experimental Results
Significance of Experimental Results
Interpret normally distributed data
2. The math scores of an exam are
normally distributed with a mean of
518 and a standard deviation of 115.
a. About what percent of the
test-takers have scores
173
between 518 and 748?
34  13.5  47.5%
b. About what percent of the test-takers
have scores less than 403?
50  34  16%
c. About what percent of the test-takers
have scores between 403 and 633?
34  34  64%
Holt McDougal Algebra 2
288 403 518 633 748 863
Significance of Experimental Results
Interpret normally distributed data
3. The heights (in feet) of fully grown
white oak trees are normally
distributed with a mean of 90 feet
and a standard deviation of 3.5 feet.
a. About what probability of white 79.5
oak trees have heights between
86.5 feet and 93.5 feet?
83 86.5 90 93.5 97
100.5
0.34  0.34  0.68
b. About what probability of white oak trees have heights between
79.5 feet and 86.5 feet?
0.0235  0.135  0.1585
c. About what probability of white oak trees have heights greater
than 93.5 feet?
0.135  0.0235  0.0015  0.16
Holt McDougal Algebra 2
Measures of Central Tendency and
Variation
Lesson 2.3 Practice A
Holt McDougal Algebra 2
Significance of Experimental Results
7.
8.
9.
10.
Holt McDougal Algebra 2