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

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

Therefore, just solve the following for x:

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

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

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

Where do you find the symbols on the computer?

Thanks

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.

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

Are my answers correct?

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.

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

What is the donation per request?