STT 421 Lecture 3 (Part II)
Material Covered in This Lecture:
•
Chapter 1, Section 1.3: Density Curves and Normal Distribution.
1
Calculations related to general normal distribution
1
2
3
Theoretical Result:
Suppose X ~ N(μ, σ). Then Z=(Xμ)/ σ ~ N(0,1)
(1).
Given a number, say a, find the area or proportion of range X ≤ a.
Solutions:
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Using the standard normal table.
0i. Find the zscore of a: z
a
=(aμ)/ σ
1ii. Find the area of range Z ≤ z
a
by using the table, where Z~N(0,1).
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Example: Suppose X~N(100, 20), find the proportion of X ≤ 80, X > 90, and
70<X<110.
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Example (Example 1.28 Example 1.29, p.7778): Suppose the SAT score has a
normal distribution N(1026, 209).
i.
What proportion of all students who take the SAT have scores of at least
820.
ii. What proportion of all students have SAT scores between 720 and 820.
*
Using MINITAB
Remember: Suppose X ~ N(
μ, σ
), Z ~ N(0,1). Then
The area of X ≤ a = The area of Z ≤ (aμ)/σ
The area of X > a = The area of Z > (aμ)/σ
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 Summer '08
 NANE
 Normal Distribution

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