Question: Let x represent the scores on a mathematics achievement test given to eighth-grade students.

Suppose that for the population of all scores on the test, the mean is µ = 50 and the standard deviation is = 15. If a random sample of 100 values of x is obtained, find the probability that the sample mean x will be between 51 and 53; that is, find P[51 < \(\bar{X}\) < 53].