4. (5%) Let and Var ( X ) denote the expectation and variance of a random variable X , respectively. Please show that

3. (10%) A teacher believes that the average grade of a class of 100 students is not higher than 85. The teacher randomly selects 64 students. The average grade of the 64 students is 87.8 and the standard deviation is 12.8. Using a significance level of 0.05, what conclusion should the teacher make?