Standard Deviation: n = 2500, mu = 50, sigma = 10

[Rocky]

My question is as follows:

If I have 2500 samples, with a mean of 50 and a standard deviation of 10, how many samples are above 60???

Thanks!!

 

[royhaas]

Your question is ambiguous. What are your assumptions?

 

[Rocky]

Assumption: normal distribution

So to put it in a more concrete form, if I have an exam that 2500 students have taken, with a mean of 50, and a std. dev. of 10, how many students scored above 60?

 

[galactus]

If you look close at your given data, you can see that \(\displaystyle x=60, \;\ {\mu}=50, \;\ {\sigma}=10\)

Doesn't the Central Theorem say that approx. 68% of the data falls within one standard deviation of the mean?. That is, 34% above the mean and 34% below the mean.

Look at your data:
60-50=10 and your SD is 10; One SD above the mean. Therefore, 60 is 1 SD above the mean.

Now, it should be easy to find the % above 60, then multiply by 2500.

 

[Rocky]

Don't I need to find the z-score, or not?

 

[galactus]

We have the z-score already...A z-score is the number of standard deviations we are from the mean. We know that is 1 because we are 1 SD above the mean.