Stats IQ scores question

Question

Assume that IQ scores are normally distributed, with a standard deviation of 16 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 1

Find z for +2 deviation:

z = (mean - population mean)/(SD/sqrt(sample size) = (2/(16/sqrt(75)) = 1.08

Because normal distribution is symmetric z for -2 deviation is -1.08

Need to find P(-1.08 < z < 1.08) = P(z < 1.08) - P(z < -1.08) = 0.8599 - 0.1401 = 0.7198