SOLUTION: How do I enter this in calculator, I feel like it should be any easy answer... Assume that IQ scores are normally distributed, with a standard deviation of 14 points and a mean of

Question 1079602: How do I enter this in calculator, I feel like it should be any easy answer...
Assume that IQ scores are normally distributed, with a standard deviation of 14 points and a mean of 100 points. If 75 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 stanbon(75887) (Show Source): You can put this solution on YOUR website!
Assume that IQ scores are normally distributed, with a standard deviation of 14 points and a mean of 100 points. If 75 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.)
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Let the sample mean = x-bar
You want P(|x-bar - 100| < 2
You want P(98 < x-bar < 102)
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z(98) = (98-100)/(14/sqrt(75)) = -1.2372
z(102) = (102-100)/(14/sqrt(75)) = +1.2372
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P(98< x-bar < 102) = P(-1.2372< z < 1.2372)
= normalcdf(-1.2373,1,2372) = 0.7840
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Cheers,
Stan H.
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