My final exam. Please help

Question

You you want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately P equals 0.31. You would like to be 96% confident that your estimate is within 3% of the true population proportion how large of a sample size is required?

Answer 1

p(1-p)z_α/2²/ME² =

0.31*(0.69)*NORM.S.inv(0.98)^2/0.03^2 =

1002.451, which rounds up to

1003