ABSTRACT
In this chapter you will:
Learn how the normal can be used as an approximation for the binomial distribution if N (the number of trials) is large.
Learn what the normal curve is, how it arose historically, and what kind of circumstances produce it.
Learn what the central limit theorem is and how the normal distribution can be used as an approximation for the distribution of sample means if N (the sample size) is large.
Be introduced to the t distribution and learn how it can be used for the distribution of sample means if N is small.
Be introduced to the standard error of the mean and learn how to perform a single-sample test, determining whether a sample was probably drawn from a population with specified parameters.
Learn how to determine 95% confidence intervals for the population mean.
In chapter 3 you were asked to derive critical values for the binomial sampling distribution for larger and larger numbers of trials. This was not too difficult to do for small values like 10 or even 15, but you can see how tedious and error-prone this could become for larger numbers. This concerned at least some 18th-century English and French mathematicians. Lacking today's high-speed electronic computers, they set out to reduce tedium in a different way, and so sought approximations for the binomial. The goal was to find a way for computing probability values that did not require deriving probabilities for all the separate outcomes of series of different numbers of binomial trials.