sample of 500 students revealed that their incomes were...

I'm stuck on this two question problem. Please help out and show me to work these types of problems.

A sample of 500 evening students revealed that their annual incomes from employment in industry during the day were normally distributed with a mean income of $30,000 and a standard deviation of $3,000. Show your work!

How many students earned more than $30,000? _______________


How many students earned between $27,000 and $33,000? _______________

Thanks

Re: Need help with this problem (please show work)

This is not a classroom, bud.

http://www.youtube.com/watch?v=WUi44eAh_mA

Just use the formula \(\displaystyle z=\frac{(x-{\mu})\sqrt{n}}{\sigma}\)

Look it up in the body of the z-table, and when it asks for 'greater than', subtract from 1.

For the 'in between' one, find the values and subtract them.

Multiply your results by how many students were sampled.

Re: sample of 500 students revealed that their incomes were.

Hello,

I still do not understand this problem. I did a range of 27,000-33,000 since the deviation was 3,000. Than I divided that by 500 students. When I spread the range over excel I came up with an answer of 250 students making more than 30,000 year. Did I do this correctly? Doesn't seem right.

Barb

Re: sample of 500 students revealed that their incomes were.

That is correct for the first one. That's because 50% were more and 50% less than 30,000.

This case, landed right on the mean and the z score is 0. Thus, 1/2 of 500 is 250.


Between 27000 and 33000. These are 1 SD above and below the mean.

Thus, by the Empirical Rule, about 68% earn in that range. .6826 to be more accurate.

Thus, 500(.6826)=341 students.

bsimeon said:

Hello,

I still do not understand this problem. I did a range of 27,000-33,000 since the deviation was 3,000. Than I divided that by 500 students. When I spread the range over excel I came up with an answer of 250 students making more than 30,000 year. Did I do this correctly? Doesn't seem right.

Barb

Click to expand...

Do you not understand what "mean" is? (I started to write "what 'mean' means" but that looks strange!) You should have been able to look at the word "mean" and immediately think "aha, half are above the mean and half are below- since there are 500, 250 are above the mean and 250 below".

HallsofIvy said:

Do you not understand what "mean" is? (I started to write "what 'mean' means" but that looks strange!) You should have been able to look at the word "mean" and immediately think "aha, half are above the mean and half are below- since there are 500, 250 are above the mean and 250 below".

Click to expand...

Halls, you commented on a post that is over 2 years old