Putting It Together

Abstract

You are interested in starting your own MENSA-type club. To qualify for the club, the potential member must have intelligence that is in the top 20% of all people. You must decide the baseline score that allows an individual to qualify. See the Decisions project on page 421. In Chapter 6, we introduced discrete probability distributions and, in particular, the binomial probability distribution. We computed probabilities for this discrete distribution using its probability distribution function. However, we could also determine the probability of any discrete random variable from its probability histogram. For example, the figure shows the probability histogram for the binomial random variable X with and From the probability histogram, we can see Notice that the width of each rectangle in the probability histogram is 1. Since the area of a rectangle equals height times width, we can think of P(1) as the area of the rectangle corresponding to Thinking of probability in this fashion makes the transition from computing discrete probabilities to continuous probabilities much easier. In this chapter, we discuss two continuous distributions, the uniform distribution and the normal distribution. The greater part of the discussion will focus on the normal distribution, which has many uses and applications.