Question 370956: Suppose that the mean salary in a particular profession is $45,000 with a standard deviation of $2,000. To what percentile does a salary of $48,000 correspond?
1.) 91st
2.) 93rd
3.) 41st
4.) 43rd
Answer by neatmath(302)   (Show Source):
You can put this solution on YOUR website!
mean=45,000 standard deviation=2000 value of concern=48,000
We can easily see that since the value of concern (48,000) is GREATER than the mean, we can rule out the last two choices.
There is no possible way a number can be greater than the mean, but less than the 50th percentile.
So, we are only focused on the first two choices as answers.
Now, we just need to convert 48,000 into a z-score, which is given as:
(x-mean)/standard deviation
or in this case:
(48000-45000)/2000=1.5
Again, using my z-score table or calculator, I can see that a z-score of 1.5 corresponds to about the 93th percentile, which is the answer.
I hope this helps!
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