Mr. Rogers - AP Statistics Objectives

Syllabus	1st Quarter	2nd Quarter	3rd Quarter	4th Quarter
	Chap 6 Probability	7&8 Binomal Distr	9 Sampling Distr	10 Conf Intervals

Unit Plan Practice Test
Latin/Greek Root Words arch--------->ancient, example: archtype;         chrono------>time, example: chronology;             -dom----------->quantity/state, example: freedom               fer-------->carry, example: transfer;               gen--------->birth, example: generate;                 luc-------->light, example lucid;                 neo--------->new, example: neonatologist;                olig--------->few, example: oligarchy;              omni--------->all, omniscient;            sym--------->together, symbol; (Statistics connection)
AP Statistics Standards III. Anticipating Patterns: (continued) A. Probability Interpreting probability, including long-run relative frequency interpretation “Law of Large Numbers” concept Discrete random variables and their probability distributions, including binomial and geometric Discrete random variables and their probability distributions, including binomial and geometric Simulation of random behavior and probability distributions Mean (expected value) and standard deviation of a random variable, and linear transformation of a random variable B. Combining independent random variables Notion of independence versus dependence Mean and standard deviation for sums and differences of independent random variables
Objectives Essential Question: Can humans simulate a random process and why is this an important issue? Ch 7.1, 7.2 -- Random Variables Be as one with the following vocabulary: random variable, discrete random variable, continuous random variable, density curve. Plot discrete probability distributions for simple systems such as flipping coins. Be as one with the law of large numbers (p. 389). Average results of many independent observations are stable and predictable (p.392) Describe the law of small numbers (p.392). Find the mean of a discrete probability distribution (p. 387). Homefun: 7.5, 7.7, 7.19, 7.23 -- Read section 7.1, 7.2	Activities Lesson 1 Key Concept: Random processes have predictable probability distributions yet true randomness is hard to simulate.   Purpose: Learn the basic principles of probability distributions. Warm up: Draw the probability distribution for flipping four coins. Find the area under the density curve for values of 1 through 3. Find the mean of the distribution. Interactive Discussion: Objectives 1-2. Discuss the results of the warm up. Stats Investigation (Teams of two):
Stats Investigation: Simulation of a Random Process ( Teams of two) Purpose: Determine if actual results of flipping a coin match results simulated by humans. Instructions: Each partner in a two person team will record 100 fake coin toss tosses on a sheet of paper using H for heads and T for Tails. The team will then record 200 actual tosses. The experimenters will then circle the runs of 2 or more heads within the data both for the fake and real tosses. For example the following data contains 2 runs of 3, 1 run of 6, and 3 runs of 2 heads: HHHTTHHHTHTHTTTHHHHHHTTTTHHTTTTHHTHH The experimenters will post the number of runs of each length on the board. When all results are posted for the class, the number of runs vs. size of runs is to be plotted for the classes fake and real data ( two separate plots). Questions /Conclusions: Answer with short paragraphs. What is the biggest difference between the real and fake data. Speculate about why this is the way it is. Are humans reliable at generating random numbers? Discuss this both in terms of the law of large numbers and the law of small numbers (p. 392) Resources/Materials: pennies for flipping
Essential Question: Can standard deviations be added? Ch 7.2 -- Random Variables Apply the rules for means on p.396. Calculate the standard deviation of a discrete random variable. (p.398). Apply the rules for variance on page 400. Homefun: 7.25, 7.31, 7.39 --	Lesson 2 Key Concept: P Purpose: B Warm up (Teams of two): D Interactive Discussion: Objectives Problem Solving (Teams of two): C
Essential Question: Do we live in a binary world? Ch 8.1 -- The Binomial Distribution Be as one with the Binomial Setting on page 416, SNIP. Calculate binomial distributions with a TI - 83 (npk - no pigs killed). Use the binomial coefficient or combinations. Calculate means and standard deviations for the binomial distr. Homefun: 8.1 to 8.4, 8.9, 8.15, 817, 8.19	Lesson 3 Key Concept: The binomial distribution Purpose: Understand how the world can be modeled as a binary system and how the binomial distribution can be used to analyze it.   Warm up: List various ways the world can be viewed as binary   Interactive Discussion: Objectives. Note that the binomial distribution is often used for analyzing surveys and for predicting election. Note that knowing the mean and probability of success for a binomial fixes both the mean and standard deviation as compared to the normal distribution where these are independent.   Individual Work: Calculate the binomial coefficient first by hand and next using the combinations feature of the TI-83 calculator 3 coins in the fountain analysis
Essential Question: When is estimating how many tries before success an issue? Ch 8.2 -- The Geometric Distribution Be aware of the key difference between binomial and geometric distributions. Be as one with the Geometric Setting on page 435, SPIT Correctly use the geometric distribution for calculating probabilities with the TI-83 calculator. Homefun: 8.25 to 8.45	Lesson 3 Key Concept: The geometric distribution Purpose: Use the geometric distribution   Warm up: List various situation when estimating the first success is important   Interactive Discussion: Objectives.   Individual Work: Solve geometric distribution problems first by hand and next using the combinations feature of the TI-83 calculator. batter problem