# Chapter 3 Constructing Statistical Intervals Assuming a Normal Distribution Using Simple Tabulations

## Objectives and Overview

This chapter presents, tabulates, and compares factors for calculating the different kinds of intervals, based upon a sample of size n from a normal distribution with unknown mean μ and unknown standard deviation σ. Specifically, we present factors for:

• Two-sided confidence intervals and one-sided confidence bounds to contain the distribution mean μ and the distribution standard deviation σ.
• Two-sided tolerance intervals and one-sided tolerance bounds to contain at least a proportion β of the distribution values, for β = 0.90, 0.95, and 0.99.
• Two-sided prediction intervals and one-sided prediction bounds to contain the values of all of m = 1, 2, 5, 10, 20, and m = n randomly selected future observations, and the sample mean and standard deviation of m = n future observations.

For each kind of interval or bound, the tables provide factors for both 95% and 99% confidence levels. We also present examples illustrating the use of these factors.

The chapter presents:

• The normal distribution, justification for its use, and background information about the factors (Section 3.1).
• The circuit pack voltage application that will be used to illustrate the use of the factors (Section 3.2).
• Use of the factors for two-sided statistical intervals (Section 3.3).
• Use of the factors for one-sided statistical bounds (Section 3.4).

## 3.1 Introduction

### 3.1.1 The Normal ...

Get Statistical Intervals, 2nd Edition now with the O’Reilly learning platform.

O’Reilly members experience live online training, plus books, videos, and digital content from nearly 200 publishers.