Please use three decimal places where applicable. I kindly ask you to personally complete the tasks without relying on AI. Additionally, provide specific, detailed steps for solving each question rather than general guidelines. Thank you.

A researcher wants to know how much time the average 11^th grader is spending on social media in one day. A random sample of 576 11^th graders is collected and the sample mean is 76.278 minutes with a standard deviation of 80 minutes.

5 points. Construct a 99% confidence interval for the population mean of social media usage per day among 11^th graders.

1 point. If we were to compute a 75% confidence interval, would this interval be wider than the interval computed above (meaning the margin of error is larger in a 75% confidence interval compared with a 99% confidence interval)? Why or why not? (Note that the t-table does not provide a way to directly compute a 75% confidence interval.)

Extra Credit 1 point. What distribution shape (symmetric, skewed right or skewed left) of the sample distribution (not population or sampling) is by far the LEAST likely and why did you choose that shape?