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# Normal distribution. S2. Rep. watch

1. I have a weird problem with this.

In the MEI June 2009 paper, question 3(i)
it says P(Z<0.2222) = 0.5878. But this is P(Z<0.222) isn't it? So does this mean that they are simply rounding 0.2222 to 0.222?

If that's true, then why, in the Jnauary 2009 paper, question 3(i) (3(i) again !!) we get P(Z<0.2146) = 0.5849?

Because P(Z<0.215) = 0.5851. So it's only NOT rounded like in the June 2009 paper.

Not to mention the tables we get ONLY GO UP TO 3 DECIMAL PLACES .

To get P(Z<0.2146), did they just look inbetween P(Z<0.214) and P(z<0.215)? It just seems ridiculous. There's no cosistency at all. Will we lose marks if we round? What's going on?
2. (Original post by Tallon)
I have a weird problem with this.

In the MEI June 2009 paper, question 3(i)
it says P(Z<0.2222) = 0.5878. But this is P(Z<0.222) isn't it? So does this mean that they are simply rounding 0.2222 to 0.222?

If that's true, then why, in the Jnauary 2009 paper, question 3(i) (3(i) again !!) we get P(Z<0.2146) = 0.5849?

Because P(Z<0.215) = 0.5851. So it's only NOT rounded like in the June 2009 paper.

Not to mention the tables we get ONLY GO UP TO 3 DECIMAL PLACES .

To get P(Z<0.2146), did they just look inbetween P(Z<0.214) and P(z<0.215)? It just seems ridiculous. There's no cosistency at all. Will we lose marks if we round? What's going on?
lok spolier.
Spoiler:
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MEOW!!
3. i think it's because around z<0.2222 a change of 0.0002 is negligible (i.e. gives such a low probability it rounds to the same value for 0.222 and 0.2222. But at higher z values the change in the probability is more sensitive due to the shape of the distribution (i.e. more data centred at the middle in a normal distribution), and for this reason a small change in z values has an effect on the probability value.

That's my hunch
4. No calculator ?
5. i think it's because around z<0.2222 a change of 0.0002 is negligible (i.e. gives such a low probability it rounds to the same value for 0.222 and 0.2222. But at higher z values the change in the probability is more sensitive due to the shape of the distribution (i.e. more data centred at the middle in a normal distribution), and for this reason a small change in z values has an effect on the probability value.

That's my hunch
This sounds very reasonable but I reckon you're giving the exam board too much credit - bet it was just an inconsistancy in their answers! In the exam if you're using the tables then you can only give the answer to the degree of accuracy that you've got... When I did it, I was told to write stuf like P(Z<0.215) = 0.5851 (from tables to 3 d.p.) so that they knew exactly where I'd got the result from!
6. (Original post by Neofytos)
No calculator ?

can't do it via calculator can you?
This sounds very reasonable but I reckon you're giving the exam board too much credit - bet it was just an inconsistancy in their answers! In the exam if you're using the tables then you can only give the answer to the degree of accuracy that you've got... When I did it, I was told to write stuf like P(Z<0.215) = 0.5851 (from tables to 3 d.p.) so that they knew exactly where I'd got the result from!

but the markscheme is doing it to 4dp, so what should I do?
8. (Original post by Tallon)
can't do it via calculator can you?
P(Z<0.222)=0.58784
P(Z<0.2222)=0.58792

There is a big range for those values and you SHOULD always give ur final answer to 3 significant figures so for both 222 and 2222 answer is 0.588
9. There is a big range for those values and you SHOULD always give ur final answer to 3 significant figures so for both 222 and 2222 answer is 0.588
3s.f. is the way forward.
3s.f. is the way forward.

but the other probably I mentioned would round to two different sf wouldn't it?
11. (Original post by Tallon)
but the other probably I mentioned would round to two different sf wouldn't it?
Tallon,dont be worried about these. Mark schemes give very high range,so "Baby dont worry,.."

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