Download AP Statistics – Day 1

Notes: The Normal Distribution
Density Curves
Normal Distribution
Normal Distribution notation
Empirical Rule
An IQ test is normally distributed
Heights of American males are
with mean 100 and standard
normally distributed with mean 69 in
deviation 15.
and standard deviation 2.5 in.
An IQ test is normally distributed with mean 100
and standard deviation 15. Just by knowing the
mean and standard deviation, we can answer the
Average American adult male height is 69 inches
(5’ 9”) tall with a standard deviation of 2.5 inches.
following questions:
What is the likelihood that a randomly selected
(1) Between what two values do approximately
68% of IQ scores lie?
(2) Between what two values do approximately
95% of IQ scores lie?
adult male would have a height less than 69
inches?
What is the likelihood that a randomly selected
adult male would have a height of less than 66.5
(3) Between what two values do approximately
99.7% of IQ scores lie?
(4) What percent of IQ scores are less than 115?
inches?
What is the likelihood that a randomly selected
adult male would have a height of greater than 74
(5) What percent of IQ scores are greater than
130?
inches?
(6) What percent of IQ scores are less than 85?
What is the probability that a randomly selected
adult male would have a height between 64 and
76.5 inches?
Illiana’s Grade
After 5 weeks of class Iliana must transfer from a stat class at Taylor to this class. Last week
was the chapter 2 test in both classes. Iliana scored a 61 out of 70. Our test was out of 100
points. What score should she be given?
Standard Normal Distribution
Standardizing and z-scores
Suppose a student has taken two quizzes in a statistics course. On the first quiz
the mean score was 32, the standard deviation was 8, and the student received a
44. The student obtained a 28 on the second quiz, for which the mean was 23 and
the standard deviation was 3. If test scores are approximately normal, on which
quiz did the student perform better relative to the rest of the class?
4 skills you must have
1.
2.
3.
4.
P(Z < z*) = .80
P(Z < z*) = .77
A married couple is employed by the same company. The husband works in a department for
which the mean hourly rate is $12.80 and the standard deviation is $1.20. His wife is employed
in a department where the mean rate is $13.50 and the standard deviation is $1.80. Both
department salaries are normally distributed.
•
Relative to their departments, which is better paid if the husband earns $14.60 and the
wife earns $15.75?
Finding Normal Proportions
1.
2.
3.
4.
What percentile is the husband located in his department?
What percent of employees in the wife’s department earn better than her?
What percent of employees in the wife’s department earn between $12.00 and $17.00?
What would the wife need to earn to match her husband’s relative position?
If the husband wanted to earn in the 95th percentile, how much should he earn per hour?
METHODS OF ASSESSING NORMALITY
Stemplot/Histogram
Boxplot
Normal Probability Plot
Data Set 1 – Ages of the presidents at inauguration
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61
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61
54
68
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64
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65
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56
46
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42
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54
51
60
61
43
55
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61
52
69
64
46
54
47
Stemplot/Histogram
Boxplot
Normal Probability Plot
Data Set 2 – The number of frost days during April at Greenwich, England, over a 65-year
period.
0
0
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0
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Stemplot/Histogram
Boxplot
Normal Probability Plot