Suppose a population distribution has a mean = 150 and a standard deviation s = 30,

Suppose a population distribution has a mean μ = 150 and a standard deviation s = 30, and you draw a simple random sample of N = 100 cases. What is the probability that the mean is between 147 and 153? What is the probability that the sample mean exceeds 153? Would you be surprised to find a mean score of 159? Why? (Hint: To answer these questions, you need to apply what you learned in Chapter 5 about Z scores and areas under the normal curve [Appendix B].) To translate a raw score into a Z score, we used this formula:

However, because here we are dealing with a sampling distribution, replace Y with the sample mean

, with the sampling distribution’s mean μ Y, and σ with the standard error of the mean.