# Normal Distribution Problems

This book introduces random variables and their probability distributions with two detailed examples. Following that, the focus is on solving normal distribution exercises. The example exercises and solutions will help students to recognize and solve the most common types of normal distribution problems. The book covers Excel functions that can replace Z tables as the primary tools for solving normal distribution problems, the NORMDIST and NORMINV functions. Using these functions make solving normal distribution problems simpler, faster, and less likely to contain errors than the Z table method.

This book is ideal for first semester statistics students.

## An Introduction to Normal Distribution Problems

First semester statistics students typically study four or five probability distributions. The first continuous probability distribution covered in almost all beginning statistics classes is the normal distribution. Students who thoroughly understand normal distributions and who have a facility for solving normal distribution problems tend to do very well with the remaining course material. The goal of this book is to provide students with that understanding and facility.

The focus of this book is first on providing students with a clear understanding of probability distributions in general and on normal probability distributions in particular. Following that, the focus is on solving normal distribution exercises. The book is divided into five sections: Probability and Random Variables, Random Number Generator, Animal Weights, Normal Distribution Exercises with Solutions and Central Limit Theorem.

The first section, Probability and Random Variables, familiarizes the student with the concept of probability and introduces random variables and their probability distributions.

The second section, Random Number Generator, covers an example of a random variable that does not have a normal distribution but clearly demonstrates the process of finding a probability distribution. In this section we plot a histogram of a set of random numbers, approximate the shape of the histogram with a rectangle, call the rectangle a probability distribution and use it to find probabilities. We represent probabilities as areas within the rectangle.

The third section, Animal Weights, covers an example of a normally distributed random variable. In this section we plot histogram of a set of animal weights, approximate the shape of the histogram with a normal curve, call the normal curve the probability distribution and use it to find probabilities. We represent probabilities as areas underneath the normal curve. In this section we also show how to use the Excel functions NORMDIST and NORMINV. We use these two functions rather than Z tables as the tools for solving normal distribution problems. We use the NORMDIST function to find probabilities associated with given normal distribution outcomes. We use the NORMINV function to find outcomes associated with given normal distribution probabilities.

The fourth section, Normal Distribution Exercises with Solutions, includes examples of normal distribution problems. Most normal distribution exercises in introductory statistics texts are one of five or six basic types. The example exercises and solutions will help students to recognize them and to solve similar problems. Screenshots are provided showing how to use the NORMDIST and NORMINV functions in Excel in the solutions. Sketches of the normal distributions referenced in the exercises are also included.

The final section introduces the central limit theorem along with an example of how normal distributions apply to sampling distributions of the sample mean.