how large of a sample is needed to estimate the mean of a normally distributed population for each of the following?a. ME= 5, sigma=40, alpha=0.01b. ME=10; sigma=40; alpha=0.01c. compare and comment on your answers to parts a and b.

Answer:a: 425b: 107c: read belowStep-by-step explanation:Assuming ME means Error:We have:n = to be determinedME = 5σ = 40α = 0.01The z-value we will use for α = 0.01 is: 2.575See attached photo 1 for the calculation of nFor the second situation, it is calculated the same way, we just have E = 10See second attached photo for the calculation of this value of n...For part c:  The sample size is much smaller for the second situation because we are allowing more error in our estimate, so we can be less accurate.  We don't need as large of a sample size if we don't want to be as accurate