(Topic 13) Do each part below for full credit in this topic. (a) In order to estimate the average GPA of students at a college, a professor takes a random sample of 57 students and finds a sample mean...

 (Topic 13)
Do each part below for full credit in this topic.

(a) In order to estimate the average GPA of students at a college, a professor takes a random sample of 57 students and finds a sample mean of 2.79 with a sample standard deviation of 1.81. Write out the formula you should use and calculate the margin of error for a 95% confidence interval.

 (b) When conducting a new poll, what is the minimum sample size you would need to be 90% confident that the population proportion is estimated to within a 0.04 margin of error? Round your answer up to the nearest whole number.