The true mean of a quiz conducted in a class of 50 students is 70 points, and the true standard deviation is 12 points. It is desired to estimate the mean by sampling a subset of the scores, without replacement.
a. What is the standard deviation of the sample mean if only 10 scores are used?
b. How large should the sample size be for the standard deviation of the sample mean to be 1% of the true mean?