- 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
This chapter is from the book
This chapter is from the book
This chapter is from the book
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:
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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:
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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.
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Figure 6.6 The bell-shaped Normal distribution curve