SOLUTION: I can not figure this out at all. I have tried many other examples and I am no where near the answer. Any help will be greatly appreciated! Assume that IQ scores are normally dist

Question 976931: I can not figure this out at all. I have tried many other examples and I am no where near the answer. Any help will be greatly appreciated!
Assume that IQ scores are normally distributed, with a standard deviation of 13 points and a mean of 100 points. If 50 people are chosen at random, what is the probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points? (Round your answer to four decimal places.)

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The sample mean must be within 2 of the population mean.
I will do one side.
z=x bar-mu/sd/sqrt (50);; z= (98-100)*sqrt (50)/sd. I am inverting the denominator and multiplying.
z=(-2)*7.0710/13= -1.0878
I want the probability z will be within -1.0878 and +1.0878.
z=0.7233. This makes sense, because 68% are within 1 sd.

The probability one person will be more than 2 points away from the population mean is high, about 87%. With a sample of 50, however, those who are on one side will be counterbalance by those on the other.
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