Consider a variable known to be normally distributed with unknown mean and known standard deviation =10.

(a) what would be the margin of error of a 95% confidence interval for the population mean based on a random sample size of 25? the multiplier for a z confidence interval with a 95% confidence level is the critical value z∗=1.960. (enter your answer rounded to three decimal places.)

margin of error =25=

(b) what would be the margin of error of a 95% confidence interval for the population mean based on a random sample size of 100? based on a random sample size of 400? (enter your answers rounded to three decimal places.)

margin of error n=100:
margin of error n=400: