Suppose IQ scores for adults follow a Normal distribution with a standard deviation of 15. A random sample of 49 adults yields an average score of 100. a) [3 points] Construct 90%, 95%, and 99% confidence intervals for . b) [2 points] What is happening to the width of the confidence intervals as the confidence levels increase? Explain why this makes sense both practically and mathematically (based upon the formula). c) [3 points] Using the known standard deviation of 15 and confidence level of 95%, construct 3 different confidence intervals based upon sample sizes 49, 100, and 225, respectively