(a) In order to estimate the average GPA of students at a college, a professor takes a random sample of 57 students and find a sample mean of 2.79 with a sample standard deviation of 1.81. Write out...

(a) In order to estimate the average GPA of students at a college, a professor takes a random sample of 57 students and find 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.