Understanding and Calculating Probability Distribution

A researcher is studying IQ levels. From past experience she knows the population mean IQ for adults is 110 and the standard deviation is 15.

a) If samples of 30 IQs are selected and the sample mean is calculated for each sample, what can be said about the sampling distribution of the sample means, and why?

b) If she takes a sample of 30 adults and measures their IQs , what is the probability that the sample mean will be within 10 points of the possible mean.

c) What is the probability that the sample mean will actually be less than the population mean by more than 5 points?

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