For a random sample of 51 students enrolled in 12 units at a particularly university, the sample average number of hours they spend studying per week was 32.3, with a standard deviation of 12.5 You may assume the students are independent of each other.

1. Find the 90% confidence interval for .
2. Does you interval from (a) suggest that it would be unusual for a student taking 12 units to study more than 38 hours a week? Explain your answer.
3. If we wanted our confidence interval to have a margin of error of 3 hours, how many students should we plan to sample? You may assume the confidence level remains the same.
4. List all assumptions needed for a confidence interval of this type.