Question 1188836
the mean of the population is 28.6
the sample size is 36.
the standard deviation of the population is 4.18.
the standard error is 4.18 / sqrt(36) = .6967 rounded to 4 decimal places.
critical z-score at two tailed alpha of .05 (.025 on each side) = plus or minus 1.96.
on the high side, 1.96 = (x - 28.6) / .6967.
solve for x to get x = 1.96 * .6967 + 28.6 = 29.966 rounded to 3 decimal places.
on the low side, -1.96 = (x - 28.6) / .6967.
solve for x to get x = -1.96 * .6967 + 28.6 = 27.234 rounded to 4 decimal places.
if the sample mean is between 26.966 and 27.234, you can assume that the population mean of 28.6 is good.
otherwise, you can assume that it is not good and that the sample mean is more likely to be closer to the real population mean.