Question 412386: How do I approach this question? Please help.
A dormitory has 1000 students' and you have determined that the average time in the shower is 10.0 minutes with a standard deviation of 2.0 minutes. The dean is considering automatic cutoffs of showers at 8 minutes. If he decides to do this, how many students will be affected?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! normal distribution is assumed.
mean is 10 minutes
standard deviation is 2 minutes.
use of the David M. Lane z-score calculator will make this easy.
http://davidmlane.com/hyperstat/z_table.html
In the top graph, enter a mean of 10 and a standard deviation of 2 and then click on the "above" box and enter 8.
The result is that 84.1345 percent of the students will be affected because those are the ones that require more than 8 minutes to finish their shower.
With a normal distribution, 50% of the scores are above the mean and 50% of the scores are below the mean.
If the dean cut off the shower at 10 minutes, 50% of the students would be affected.
Without knowing what tools you have at your disposal, it's difficult to give you an answer that suits your situation exactly.
If you are just using the z-score tables, then the derivation of the result is harder.
To use the tables, you need to convert the problem as given to a z-score.
The derivation of the z-score would make the mean equal to zero and the standard deviation equal to 1.
A score of 8 would then translate to an equivalent z-score.
Once you know that, you would then look up that value in the z-score table and look at the percentage of scores that would be to the right of that.
It's a lot messier, but can be done.
If you let me know what tools you have at your disposal, I can probably guide you to how to get the right answer.
The answer should be what I just showed you, regardless of the method you use.
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