for problem c it is all about length of confidence interval. for 1-3 its all about central limit theorem

1. Do we always add or subtract from 0.50? Explain. 2. When do we add the corresponding area of the z-score to 0.50? 3. When do we add the two corresponding areas of the z-score?C. Solve the following problems. 11. In a group presentation, the average geometric reasoning of Grade 10 students in a Mathematics camp was observed to be 80 with s standard deviation of 4. A researcher wants to replicate the study to estimate the true population mean a to within 0.5 maximum error. If the 98% level of confidence is adopted, how many respondents are needed? 12. Teacher Carol, wants to conduct a survey about the average number of students in a certain school who wants online class instead of distance modular learning. If she plans to use 99% confidence level, 0.5 as the margin of error, and a standard deviation of 5. How many sample sizes does she need for the survey