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wplummer · Mar 22, 2009, 08:30 AM

Setting µ = 60 and σ = 7 What score falls at z = -1.96

galactus · Mar 22, 2009, 09:26 AM

The z-score is $z=\frac{x-{\mu}}{\sigma}$

Therefore, just solve the following for x:

$-1.96=\frac{x-60}{7}$

wplummer · Mar 22, 2009, 02:20 PM

What is the probability of 59? What is the probability of 62?

wplummer · Mar 22, 2009, 02:21 PM

What is the probability of 59?
What is the probability of 62?

Where do you find the symbols on the computer?

Thanks

galactus · Mar 22, 2009, 03:16 PM

Just plug in x=59 and x=62 into the formula, get the z score and look it up the probability in the table. That's it.

What symbols are you referring to on the computer? If you mean the LaTex I displayed, that is a matter of typing in the code.

To see the LaTex code I used, click on 'quote user' at the bottom of the post.

wplummer · Mar 22, 2009, 04:03 PM

What is the probability of 59? P = 2.95
What is the probability of 62? P = 2.5

Are my answers correct?

galactus · Mar 22, 2009, 04:07 PM

No ,sorry to say, probabilities are between 0 and 1, inclusive.

I will do one and you do the other, OK?

$\frac{59-60}{7}=\frac{-1}{7}\approx -.14$

That is the z-score. Now, go to the table and see that is corresponds to .4443.

That is the probability.

galactus · Mar 22, 2009, 04:15 PM

Just for kicks, the reason we look these up in a already made table is because the formula to calculate them is very difficult.

It is $\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{z}e^{\frac{-t^{2}}{2}}dt$

You do not have to worry about this. It is beyond your level of study. I just thought I would show it to you for curiosity.

If we actually use the formula(I will use my Voyage 200) to find the probability, we get:

.443201502709

Which is very close to the value in the table due to rounding -1/7 to -.14

wplummer · Mar 22, 2009, 04:17 PM

What is the donation per request?