The standard IQ test is designed so that the mean is $100$ and the standard deviation is $15$ for the population of all adults. We wish to find the sample size necessary to estimate the mean IQ score of statistics students. Suppose we want to be $90$% confident that our sample mean is within $2$ IQ points of the true mean. Assume then that $\sigma = 15$ and determine the required sample size. (Be sure to round correctly!)

Answer: