The IQ, X, of humans is approximately normally distributed with mean = 100 and standard deviation

The IQ, X, of humans is approximately normally distributed with mean μ = 100 and standard deviation σ = 15. Compute the probability that a simple random sample of size n = 10 results in a sample mean greater than 110. That is, compute P(x̅ > 110).

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Approach The random variable X is approximately normally distributed, so the sampling distribution of X will be normally distributed. Verify the independence requirement. The mean of the sampling distribution is x = , and its standard deviation is = Convert the sample mean x = 110 to a z-score and then find the area under the standard normal curve to the right of this z-score. n