6 Probability Distributions

Probability Distributions

Overview

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SAT Scores and AP Exam Scores

The College Board publishes a comprehensive collection of measures regarding SAT scores. In this chapter, we use some of the measures published by the College Board to help learn about probability distributions.

In the Section 6.1 exercises, we construct the probability distribution for student performance on the Statistics AP exam.
In Section 6.2, we find the binomial mean, variance, and standard deviation of students taking the Natural Sciences subject SAT exam who have taken high school chemistry.
In the Section 6.4 exercises, we examine graphs of the probability distribution of Critical Reading SAT scores.
In Section 6.5, we learn how to find probabilities and scores associated with performance on the Math SAT.
Finally, in the Section 6.5 exercises, we compare performance of females and males on the Writing SAT exam.

THE BIG PICTURE

Where we are coming from and where we are headed …

In Chapter 5, we learned about probability, which allows us to quantify the uncertainty involved in performing statistical inference in later chapters.
However, we first need a new set of tools in our probability toolbox: random variables and probability distributions. Here, in Chapter 6, we learn these new tools, including the binomial distribution and the normal distribution.
Chapter 7, “Sampling Distributions,” is a pivotal chapter in which we learn that statistics have predictable behavior, which allows us to perform the statistical inference we learn in the remainder of the book.