Direcions: Solve each problem on a separate sheet of paper. Show your complete solution to support your answer.

1. The average height of 35 Grade 12 students of Candon National High School is 144 cm. If the population standard deviation is 10 cm, find the confidence interval of the mean height of ali the Grade 12 students using 99% confidence level.

2. The scores of students in a Math test forms a norma distribtion. A sample of 12 scores was selected randomly. The computed sample mean and standard deviation are 50 and 10 respectively. Find the confidence interva of the population mean score adopting a confidence level of 90%?

3. A previous study showed that the average algebraic reasoning of Grade ll students is 82 with a standard deviation of 5. If a researcher wants to replicate the study to estimate the population mean to within an error of 1.1 of its true vaue. Using 95% confidence level, what is the sample size that he needs?

4. The head of a school clinic wishes to estimate the average height of all Grade 7 students. She wants to be 99% confident that the estimate is accurate to within 8 cm of the population mean. If the standard deviation of the target population from the previous study was 30 cm, how large is the sample that she needs.