# Chapter 4 Methods for Calculating Statistical Intervals for a Normal Distribution

## Objectives and Overview

This chapter extends the results of Chapter 3 and gives general methods for calculating various statistical intervals for samples from a population or process that can be approximated by a normal distribution.

The chapter explains:

• How to compute a confidence interval for a normal distribution mean, standard deviation, or quantile (Sections 4.2, 4.3, and 4.4).
• How to compute a confidence interval for the distribution proportion less (greater) than a specified value for a normal distribution (Section 4.5).
• How to compute a tolerance interval to contain a specified proportion of a normal distribution (Section 4.6).
• How to compute a prediction interval to contain a single future observation or the mean of a specified number of future observations from a normal distribution (Section 4.7).
• How to compute a prediction interval to contain at least k of m future observations from a normal distribution (Section 4.8).
• How to compute a prediction interval to contain the standard deviation of a specified number of future observations from a normal distribution (Section 4.9).
• The importance of the assumption of a normal distribution and when the construction of an interval is (and is not) robust to this assumption (Section 4.10).
• How to assess the validity of the assumption of a normal distribution and methods for constructing statistical intervals when the data cannot be described ...

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