Normal Distribution Question

In order to find the Z Value, we use the formula ^{x - mean}/s.d. So
^{8 - 7.15}/_0.88 = z value. But why is 8 used as x, rather than 8.5? I was taught if you're finding for less than x, you use x+0.5, and -0.5 when greater, because it has something to do with including the whole range of the value,x i think. Sorry I don't quite remember the whole explanation for it

What kind of calculators are you allowed to have? Casio F991EX has this kind of function built in.

In order to find the Z Value, we use the formula ^{x - mean}/s.d. So
^{8 - 7.15}/_0.88 = z value. But why is 8 used as x, rather than 8.5? I was taught if you're finding for less than x, you use x+0.5, and -0.5 when greater, because it has something to do with including the whole range of the value,x i think. Sorry I don't quite remember the whole explanation for it

just use the normal distribution on your calculator, you can do the whole question in under like 30 seconds

You're thinking of continuity correction but that's only used when you approximate a discrete distribution using a continuous distribution.

Here you have a normal distribution and you're finding the probability direct from that distribution so no approximation is occurring here.

my calculator doesn't have that function, plus we need to show our working out for the whole question

just use the normal distribution on your calculator, you can do the whole question in under like 30 seconds

I assume you're doing new spec. Old spec is different where they always have to standardise and use tables.

Ah I see, my bad.

It's a common occurrence on TSR - old spec stats is quite different to new spec so it can cause confusion

I never knew there was an even older spec haha. I am still doing the old style maths papers as we are the last year group to be doing the modular system. I've already done S1 and now I'm doing S2 and we pretty much do everything on the calculators xD

Hmm I was talking about modular (old) compared to linear (new). In modular you have to standardise and use tables for Edexcel stats. Which exam board are you using? I thought it was the same for all of them...

I'm doing AQA and we can get the answers directly from the calculator and write the answer down in the exam without any working and it will still get full marks (obviously as long as its correct). I did that for S1 last year and got 100ums. I would have thought it is the same across all boards?

We are still given the statistics table of values for all the distributions in the exam but we don't have to use it (normal, poisson, binomial etc)

Thanks for this - it turns out I was wrong! I've never taught modular spec stats so I assumed incorrectly.

Quote at the top of mark schemes:

"Where the answer can be reasonably obtained without showing working and it is very unlikely that the correct answer can be obtained by using an incorrect method, we must award full marks".

This will apply to these types of stats questions. But, I would advise students to use the standardisation method because marks are awarded for it. Just using a calculator and getting a wrong answer for whatever reason will give 0 marks. A calculator would be useful for checking answers are correct though.

Of course it's possible to get 100 UMS just using your calculator like you did but I would not recommend it.

This all applies to modular (old) spec stats for anyone reading this. For new spec it is fine to use a calculator and no marks will be awarded for working.