In #ALevelMaths #MathsToday we did the normal approximation to the binomial distribution. Why? Because it's on the spec. Why is it on the spec? No frigging idea. The binomial calculator function has rendered it useless. - ThreadSky

ecrmaths.bsky.social • 58 days ago

In #ALevelMaths #MathsToday we did the normal approximation to the binomial distribution.
Why? Because it's on the spec.
Why is it on the spec? No frigging idea. The binomial calculator function has rendered it useless.

Comments

missradders.bsky.social•58 days ago

So annoying.

mathforge.org•58 days ago

Everything is an approximation, so picking a good approximation is a wise skill to learn. Binomial is computationally nasty, so knowing that you can replace it by something far simpler is useful.

alexjw.bsky.social•58 days ago

Difference between two binomial proportions?

ecrmaths.bsky.social•57 days ago

Could you give an example of what you mean?

alexjw.bsky.social•57 days ago

https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Mostly_Harmless_Statistics_(Webb)/09%3A_Hypothesis_Tests_and_Confidence_Intervals_for_Two_Populations/9.03%3A_Two_Proportion_Z-Test_and_Confidence_Interval

theteacherwins.bsky.social•58 days ago

Agree!!!
Although some good learning about why p has to be close to 0.5 as well as what the continuity correction is and why it’s needed.

ecrmaths.bsky.social•58 days ago

The continuity correction isn't even on AQA, which I think makes it even less relevant!

theteacherwins.bsky.social•58 days ago

Really??? 🤯
We’re edexcel.
So you ignore going from discrete to continuous?

ecrmaths.bsky.social•58 days ago

Yep. We just do the conversions (np, np(1-p), etc) and discuss the requirements (n large, p near 0.5, np and n(1-p) above 5, etc) and don't really do any actual calculations 🤨

theteacherwins.bsky.social•58 days ago

The new calculators have rendered a lot of the approximations useless - Poisson to binomial, normal to Poisson…

susanwhitehouse.bsky.social•58 days ago

Absolutely useless as a way of calculating binomial probabilities. But it is worth the students realising that the binomial distribution with p=0.5 and an infinite number of trials is the normal distribution. That's the only use I have for teaching this bit of the topic these days.

ecrmaths.bsky.social•58 days ago

Yes, I suppose it's nice to see the connection between the different distributions. Like the t-distribution becoming the normal distribution as the degrees of freedom tends to infinity...

adgonvel.bsky.social•58 days ago

That’s me tomorrow…

cuddlefishj.bsky.social•57 days ago

I don’t teach anymore, but when I did, it made sense because we bang on so much about z-scores, and the shape of the Normal distribution that it is kinda cool to compare it with its similar shaped cousin…

paddymacmahon.com•57 days ago

A scratchcard has a one in 50 chance of winning a prize. What's the minimum number of times I need to play to have a better than 50% chance of winning at least 10 prizes?

paddymacmahon.com•57 days ago

Maybe 50% isn't the best choice of probability to ask for in terms of having to deploy a normal approximation. What's the minimum number of scratchcards I need to buy in order to have a greater than 80% chance of winning at least 10 prizes?

ecrmaths.bsky.social•57 days ago

I'm not sure how you'd do a normal approximation for that kind of question... what would you use for μ and σ? Are you using inverse normal/percentage points?

paddymacmahon.com•57 days ago

Yes, inverse normal: a normal approximation gives a pretty good value (n=622) such which we can refine with the binomial calculator.

Actual answer is 625 in this case.

mathforge.org•57 days ago

#WellActually

ecrmaths.bsky.social•57 days ago

Ahh I see now, thanks! Well, that does seem like a good use of the approximation; I retract my claim that it is completely useless 😊

roserover.bsky.social•58 days ago

Could say the same thing for coding with spreadsheets and calculators. They need to tidy up the whole A level but especially stats (large data set 😖)

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