# Thread: Normal Distribution

1. ## Normal Distribution

I'm having trouble with this problem

any whelp will be appreciated

2. Originally Posted by BkNekno
I'm having trouble with this problem

any whelp will be appreciated
Where are you stuck? Have you been taught how to calculate probaiblities from a normal distribution? I'll do (b):

$Z = \frac{X - \mu}{\sigma}$.

z-score for 130: $z = \frac{130 - 172}{33} = -1.2727$.

z-score for 210: $z = \frac{2110 - 172}{33} = 1.1515$.

Therefore Pr(130 < X < 210) = Pr(-1.2727 < Z < 1.1515)

= Pr(Z < 1.1515) - Pr(Z < -1.2727)

= Pr(Z < 1.1515) - Pr(Z > 1.2727) by symmetry

= Pr(Z < 1.1515) - [1 - Pr(Z < 1.2727)] = Pr(Z < 1.1515) + Pr(Z > 1.2727) - 1.

Now use your tables to get the required probabilities.

3. well the thing is that the teacher just keep talking n talking n writing non-stop in the board all the time all i can do is copy the notes.
Also i got a question
For example:
Mean = 30 and standard deviation = 4
P(X<37) = P(Z> 37-30/4) = P(Z<1.75) = 0.5 + 0.4599 = 0.9537

So my question is where does that 0.5 come from that is also confusing me.
Also there is 2 different table i'm just not sure which one to use most of time

This is table 2

This is table 3

Thanks for your help

4. Originally Posted by BkNekno
[snip]
Also i got a question
For example:
Mean = 30 and standard deviation = 4
P(X<37) = P(Z> 37-30/4) = P(Z<1.75) = 0.5 + 0.4599 = 0.9537

So my question is where does that 0.5 come from that is also confusing me.
Also there is 2 different table i'm just not sure which one to use most of time

This is table 2

This is table 3

Thanks for your help
Table A-2 gives area to the left of the z-value, that is, Pr(Z < z) (but you have to add 0.5 to the value in the table - that's just how the table works).

Table A-3 gives area to the right of the z-value, that is, Pr(Z > z).

Using Table A-2: Pr(Z < 1.75) = 0.5 + 0.4599 = 0.9537. The 0.5 is added because that's how Table A-2 works.

Using Table A-3: Pr(Z < 1.75) = 1 - Pr(Z > 1.75) = 1 - (look it up in the table) = 0.9537.

It doesn't matter which table you use as long as you understand how to use it.

5. so that is how it work thank you very much !!