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# Normal distribution help

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1. The question is find P(X < 8.6), with mean 8 and standard deviation 5.

So I standardised it and got that z = 0.12

I looked up the z score for 0.12 on the table and it says 0.4522 which is wrong. The answers 0.5478, am I reading the table wrong??? Because it doesn't say 0.5478 anywhere even though I know that's the answer...

This is the table. Thanks!

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2. (Original post by JellyCat99)
The question is find P(X < 8.6), with mean 8 and standard deviation 5.

So I standardised it and got that z = 0.12

I looked up the z score for 0.12 on the table and it says 0.4522 which is wrong. The answers 0.5478, am I reading the table wrong??? Because it doesn't say 0.5478 anywhere even though I know that's the answer...

This is the table. Thanks!

Posted from TSR Mobile
Your table is not appearing. It should indeed be 0.5478.

Your answer is 1-0.5478 though which is P(X>8.6). Perhaps your table is giving you values that are P(Z>z) rather than the conventional P(Z<z)? I'd have to see the table in order to confirm.

3. You are using the wrong Standard Normal Distribution table.

You are using the "reverse" of the table you should be using.

Note in this image (the table you may had been using):

Image source:
https://onlinecourses.science.psu.ed...rmalBTable.gif

You require the Standard Normal Distribution Table where:
, (where is the cumulative distribution function).

i.e. the area under the curve is swept out FROM THE LEFT.

The second post, by RDKGames, shows what you need to do.

(Note that:
,
so that:
,
should be greater then 0.)
4. (Original post by simon0)
You are using the wrong Standard Normal Distribution.

You are using the "reverse" of the table you should be using.

Note in this image (the table you may had been using):

Image source:
https://onlinecourses.science.psu.ed...rmalBTable.gif

You require the Standard Normal Distribution Table where:
, (where is the cumulative distribution function).

i.e. the area under the curve is swept out FROM THE LEFT.

The second post, by RDKGames, shows what you need to do.

(Note that:
,
so that:
,
should be greater then 0.)
Yeah I had a closer look at the table they give us and you're completely right, I'd just never had to use a table with the probabilities shown in this style before. Thanks!

Posted from TSR Mobile

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