- Random Numbers and Probability Distributions
- Casino Royale: Roll the Dice
- Normal Distribution
- The Student Who Taught Everyone Else
- Statistical Distributions in Action
- Hypothetically Yours
- The Mean and Kind Differences
- Worked-Out Examples of Hypothesis Testing
- Exercises for Comparison of Means
- Regression for Hypothesis Testing
- Analysis of Variance
- Significantly Correlated
- Summary

## Normal Distribution

The Normal distribution is one of the most commonly referred to distributions in statistical analysis and even in everyday conversations. A large body of academic and scholarly work rests on the fundamental assumption that the underlying data follows a Normal distribution that generates a bell-shaped curve. Mathematically, Normal distribution is expressed as shown in Equation 6.1:

Where *x* is a random variable, μ is the mean and σ is the standard deviation. The standard normal curve refers to 0 mean and constant variance; that is, σ = 1 and is represented mathematically as shown in Equation 6.2:

I generate a regular sequence of numbers (*x*) between –4 and 4. I can transform *x* as per Equation 6.2 into *y*. The plot in Figure 6.6 presents the standard normal curve or the probability density function, which plots the random variable *x* on the x-axis and density (*y)* on the y-axis.

Figure 6.6 The bell-shaped Normal distribution curve