Central limit theorem: Sample mean
A worldwide organization of academics claims that the mean IQ score of its members is , with a standard deviation of . A randomly selected group of members of this organization is tested, and the results reveal that the mean IQ score in this sample is . If the organization's claim is correct, what is the probability of having a sample mean of or less for a random sample of this size?
Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.