z-test or normal distribution
n=20, x̄ =89, s=2.0, 99%
x̄ -z_alpha/2(s/square root of n)< µ< x̄ +z_alpha/2(s/square root of n)
89-(2.575)(2.0/square root of 20)< µ< 89-(2.575)(2.0/square root of 20)
87.848< µ< 90.152
margin of error:
the critical value is 2.575.
the standard deviation is 2.0 (from the question), but as this is a sample, we need the standard error for the mean.
the formula for the se of the mean is standard deviation / √(sample size), so: 2.0/ √(20)=0.447.
me=2.575 * 0.447 = 1.151.
therefore, the margin of error is 1.151 with the confidence interval of 87.848< µ< 90.152.
in every door a person can enter or leave.
multiply to the number of doors.