Ask Uncle Colin: why does the normal distribution stop at $z=\pm 4$?

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions -- and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can.

Dear Uncle Colin,

In Statistics, we were shown a picture of the standardised normal distribution curve, and the base stops at +4 and -4. Why is it not $\pm 5$, $\pm 10$, or anything else? Is there something special about 4?

-- Got An Unanswered Statistics Struggle

Dear GAUSS,

The standard normal distribution goes on forever in both directions — which means you can’t possibly draw the whole thing, and you need to choose a window.

From -4 to 4 is a decent choice (there’s very little area left in the tails beyond that, and it’s more than good enough for all S1 — purposes), but you could take it out as far as you liked, or do it more narrowly (I don’t think I’d expect to see a z-score beyond ±3 in S1).

Hope that helps!

-- Uncle Colin

Colin

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.

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