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 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


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 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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