Statistics problem

Question

How large of a sample must be drawn so that 98% confidence interval for μ will have a margin of error equal to $133 and σ=$530

Answer 1

margin of error for a sample mean = z critical for 98% CI * sigma/square root (sample size)

z critical for 98% CI = 2.33

margin of error given as 133 and sigma given as 530 so

133 = 2.33 * 530/square root(SS)

square root(SS) = 2.33 * 530/133

SS = (2.33 * 530/133)**2 = 86.21, so will need to draw a sample size of 87