Statistics Homework Help (the empirical rule)

[ksinclair]

Hello
My name is Krista and I am new to this platform. I need some help with the empirical rule. This is the third chapter of my statistics course and I was doing pretty good until I got to this section. I have read over how to compute the data but I am just not getting it.

The problem in my homework assignment is as follows:

SAT math scores have a bell shaped distribution with a mean of 515 and a standard deviation of 114.

I need to:
a) Find the percentage of SAT scores that is between 401 and 629.
b) Find the percentage of SAT scores that is less than 401 or greater than 629.
c) Find the percentage of SAT scores that is greater than 743.

I have read the sections that explains I need to draw a graphic to illustrate the data. That is what I am not understanding. The graph must be roughly bell shaped and the mean goes in the middle of the graphic with the standard deviation on both sides represented in integers. I hope I included enough information I am so confused I am not sure what to add that may help.
Thank you very much for helping me...anyone?

 

[galactus]

When you find a percentage 'between', then find your percentages in the z table and subtract them.

But, it would appear these problems are designed to use the Empirical Rule. It says that 68% of the data falls within one Standard deviation from the mean, 95% falls within 2 S.D. from the mean, and 99.7% falls within 3 S.D. froom the mean.

Like so, here is a start for the first one.

So, using \(\displaystyle z=\frac{x-{\mu}}{\sigma}\)

\(\displaystyle \frac{401-515}{114}=-1\)

\(\displaystyle \frac{629-515}{114}=1\)

See there?. A score of 401 is one standard deviation below the mean and a score of 629 is one standard deviation above the mean.

Therefore, by the Empirical Rule, about 68% fall in that range.

That is what a z score measures...how many standard deviations the data falls above or below the mean.

You try ther other two and let me know what you get.