'Numbers rule the universe' -- (Pythagoras, c



AP Statistics 2017-2018

Chapter 2: The Normal Distributions

2.1: Density Curves and the Normal Distribution

2.2: Standard Normal Calculations

"The science of pure mathematics, in its modern developments, may claim to be the most original creation of the human spirit." -- (Alfred North Whitehead, 1861-1947)

Eratosthenes (276-194 B.C.): This Greek mathematician calculated the circumference of the earth with an error of less than 2%. The computational process and reasoning used by Eratosthenes involved simple geometric reasoning that is taught in modern secondary school geometry classes.

Assignment # 1 (§2.1) M:[9-18-17]

Read pp. 78-83: KNOW:

• what a mathematical model is

• the definition of a density curve is

• what a normal curve is

• where the mean and the median are for a normal curve

• the impact of skewing in the mean and median

Do: p. 83 - 84 # 2.1 - 2.4

Assignment # 2 (§2.1) T:[9-19-17]

Read pp. 85 – 88: KNOW:

• what a normal distribution looks like

• what [pic] and [pic]are

• the effect of different sizes of [pic]on the shape of the distribution

• where the inflection points are

• what the 68-95-99.7 rule is

Do: pp. 89 # 2.6 – 2.7

Assignment # 3 (§2.1) W:[09-20-17]

Read p. 90.

pp. 89 # 2.8 – 2.9

pp. 90 – 92 # 2.11 – 2.15

Assignment # 4 (§2.2) M:[09-25-17]

Read pp. 93 – 95; pp. 96 – 102.

p. 95 # 2.19

pp. 103 – 104 # 2.21 – 2.25

Assignment # 5 (§2.2) T:[09-26-17]

Read pp. 104 - 108

pp. 108 – 109 # 2.26 – 2.27

pp. 109 – 111 # 2.28 – 2.33

Assignment # 6 (§2.2) W:[09-27-17]

Read p. 109; p.112

pp. 109 – 111 # 2.34 – 2.36

pp. 113 – 117 # 2.39 – 2.49 odd

Assignment # 7 (§2.1-2.2 Review) Th:[09-28-17]

pp. 113 – 117 # 2.38 – 2.54 even

Assignment # 8 (Practice Test) F:[09-29-17]

Take-home Study Quiz

Assignment # 9 (Chapter 2 Test) M:[10-02-17]

Read and perform p.120/ACTIVITY 3

Key Words, Skills, Terminology and Concepts

|Normal Distribution |Density Curve |Mathematical Model |Median and Density Curve |Mean and Density Curve |

|[pic] and [pic] |Inflection Points |68-95-99.7 |N([pic],[pic]) |Standard Normal Distribution |

| | |Empirical Rule | | |

|Standardizing and |Boxplot (Box-whisker plot) |Standard Normal Tables |Areas and the Normal Proportions|Assessing Normality |

|z-scores | | | | |

|Normal Probability Plot |[pic] | | | |

Usage of the TI-83 – MATH PRB 5:RandInt; RandInt (Low #, High #, # of numbers); STO ( ; 2nd ENTER; Writing a simple program PRGM ; Graphing The Standard Normal Curve - equation & 2nd DISTR DISTR 1:normalpdf( ; Normal Probability Plot; STAT 5: SetUpEditor; 2nd DIST DRAW 1:ShadeNorm (begin x, end x, mean, std. dev.); 1:ShadeNorm (begin z, end z); 2nd DIST DISTR 2:nomalcdf (begin x, end x, mean, std. dev.) – finding probability/area with z-values; 2nd DIST DISTR 2:nomalcdf (begin z, end z) - finding probability/area with z-values; 2nd DIST DISTR 3:invNorm (percentile, mean, std. dev.) - finding an x-value; 2nd DIST DISTR 3:invNorm (percentile) – finding a z-value.

"I have not been in this country very long, but I do know this. For a 16-year old, low-income Hispanic kid growing up in East Los Angeles, there are a lot of things that are dangerous. Calculus is not one of them." -- (Jaime Escalante)

The Greek Age of Reason extended from roughly 600 B.C. to 300 B.C. There was the realization that humans have intellect, and that through observation and experimentation, the human mind can discover truths. Mathematics became a useful tool in this discovery process. Greeks such as Pythagoras, Plato, Aristotle, Euclid, Eratosthenes, Archimedes, and others began to develop this magnificent academic discipline in their attempts to understand the universe as they knew it.

"The advancement and perfection of mathematics are intimately connected with the prosperity of the state." --

(Napoleon Bonaparte, 1769-1821)

Archimedes (c. 287-212 B.C.): Considered one of the greatest mathematicians of all time, he produced a very accurate computation of pi and was the first to determine the volume of a sphere. He also developed laws of hydrostatics that included mathematical analysis related to pressure on bodies placed in water.

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