An IQ test is designed so that the mean is 100 and the standard deviation is 8 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 99% confidence that the sample mean is within 2 IQ points of the true mean. Assume that =8 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.