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The Practice of Statistics - Starnes, Tabor, Yates, & Moore
Chapter 2: The Normal Distributions
Key Vocabulary:
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density curve
µ mu
σ sigma
normal curve
normal distribution
Calculator Skills:
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normalpdf(x, µ, σ)
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N ( µ ,σ )
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standardized value
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inflection point
68-95-99.7 rule
percentile
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z-scores
standard normal
distribution
normal probability plot
normalcdf(lowerbound, upperbound, µ, σ)
EE (1E99 and -1E99)
invNorm(area, µ, σ)
1. What is a percentile?
2. Is there a difference between the 80th percentile and the top 80%? Explain.
3. What is the difference between frequency, and relative frequency?
4. What is a cumulative relative frequency graph?
5. Describe how to find the value at a given percentile on a cumulative relative frequency
graph.
Chapter 2: The Normal Distributions
The Practice of Statistics - Starnes, Tabor, Yates, & Moore
6. Explain what is meant by standardizing a variable.
7. What does a z-score represent?
8. What does it mean to “transform” data?
9. When we are transforming data, what happens to the shape, center, and spread of a
distribution when we add or subtract a constant from each observation in the data set? Be
specific.
10. What happens to the shape, center, and spread of a distribution when multiply or divide each
observation by a constant? Be specific.
11. How do these transformations affect our z-scores?
12. What is a density curve?
Chapter 2: The Normal Distributions
The Practice of Statistics - Starnes, Tabor, Yates, & Moore
13. What does the area under a density curve represent?
14. Where is the median of a density curve located?
15. Where is the mean of a density curve located?
16. How would you describe the shape of a normal curve? Draw several examples.
17. Where on the normal curve are inflection points located?
18. What is a normal distribution?
19. What is the standard normal distribution?
20. What is the 68-95-99.7 rule? What does it represent?
21. What information does the standard normal table give?
Chapter 2: The Normal Distributions
The Practice of Statistics - Starnes, Tabor, Yates, & Moore
22. How do you use the standard normal table (Table A) to find the area under the standard
normal curve to the left of a given z-value? Draw a sketch.
23. How do you use Table A to find the area under the standard normal curve to the right of a
given z-value? Draw a sketch.
24. How do you use Table A to find the area under the standard normal curve between two given
z-values? Draw a sketch.
25. If you are given the area under a curve, how do you find the observed value that corresponds
to it? Draw a sketch.
26. Describe a method for assessing whether or not a distribution is approximately normal.
27. What is a normal probability plot?
Chapter 2: The Normal Distributions
The Practice of Statistics - Starnes, Tabor, Yates, & Moore
28. What does it mean if the points on a normal probability plot lie close to a straight line?
29. How do outliers appear on a normal probability plot?
Chapter 2: The Normal Distributions