Section 54 Normal Distribution: Properties

54.1 Properties

• Gaussian / Normal distribution

• Also known as Bell curve

• It is symmetric around the point \(x=\mu\)

• \(Mean = Median = Mode\)

• It is unimodal

• The area under the curve and over the x-axis is unity

• \[ \large P(\mu - 1.64\sigma < X < \mu + 1.64\sigma) = 0.90 \]

• \[ \large P(\mu - 1.96\sigma < X < \mu + 1.96\sigma) = 0.95 \]

• \[ \large P(\mu - 2.58\sigma < X < \mu + 2.58\sigma) = 0.99 \]