SOLUTION: Assume that IQ scores are normally distributed, with a standard deviation of 12 points and a mean of 100 points. If 100 people are chosen at random, what is the probability that th

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Question 865869: Assume that IQ scores are normally distributed, with a standard deviation of 12 points and a mean of 100 points. If 100 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?
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!


Hi

mean = 100, SD = 12 for population

Sample of 100:  s = 12/sqrt(100) = 1.2

P(x ≤ 10)

z = -2/12/sqrt(100)= -2/1.2 = -1.6667 = 4.78%

P(x ≤ 14) 

z = 1.6667 = 95.22

 P(10 ≤ x ≤ 14) = 95.22 - 4.78 = 90.44

Or

P(10 ≤ x ≤ 14)= normalcdf(10,14, 100,1.2) 

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