Quick questions on z-scores, standardisation and comparing normal distributions for HSC Maths Standard 2

1short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is standardising a value, step by step?

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Standardising means carrying a raw value across to the common z-scale. The diagram below maps a test mark of

85

(on a test with

\mu = 70

\sigma = 12

) down to its z-score. The two parts of the formula are two moves on the picture. Subtracting the mean slides the marked value across relative to the centre.

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