Answer the following

ACTIVITY 2: Compute Me! Direction: Solve the following problems. Assume that the population is infinite in each case. Show the solution in a step-by-step procedure. 1. Individual students' scores on a national test have a normal distribution with a mean of 18.6 and a standard deviation of 5.9. At a Trade School, 76 students took the test. If the scores at this school have the same distribution as national scores, what is the mean and standard deviation of the sample mean for 76 students? 2. In 2019, the mean return of all common stocks on the Philippine Stock Exchange was 3.5%. The standard deviation of the returns was about 26%. A finance student forms all possible portfolios that invested equal amounts in 5 of these stocks and recorded each portfolio's return. This return is the average of the returns of the 5 stocks chosen. What are the mean and standard deviation of the portfolio returns? Activity 3: Perform Me! WRITTEN WORK For this week's assessment, you must answer this activity as your written work. To do the task, take note of the learning competency, the question to be answered, and the rubric on how you will be evaluated. You must complete the three parts: CLAIM, EVIDENCE, and REASONING. On CLAIM, you will state your stand about the question; on EVIDENCE, you will provide data supporting your claim; and on REASONING, you must state mathematical concepts/ideas that could justify the claim. Learning Competency: illustrate the Central Limit Theorem. If a sample is drawn from a population, what happens to the standard QUESTION error of the mean and the shape of the distribution if the sample size is increased from 50 to 200? CLAIM EVIDENCE REASONING