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[h]SL 4.12 Standardization of normal variables
[q] Distribution
[a] All normal distributions can be viewed in the same way, if we consider it with a centre of μ and measure x-values by how many standard deviations (σ’s) away from μ they lie. Standardising a normal distribution is when we shift the mean to μ = 0 and set σ= 1 Then, Simply, x-values become a measure of how many σ’s away from μ they are, and we call these new, standardised, x-values z-scores.
To do this, we use the formula: \(z= \frac{x-μ}{σ }\), where x is the original x-value, and μ & σ are the original mean & s.d. This process will be most helpful for finding an unknown μ or σ, with the help of inverse norm.
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