Question 1168750
<font color=black size=3>
Given information:
mean = xbar = 78
standard deviation = sigma = 2.3
sample size = n = 30
confidence level = 99%


A 99% confidence level means the critical value is approximately z = 2.58 which you find using a calculator or table.


The lower value of the confidence interval is
L = xbar - z*sigma/sqrt(n)
L = 78 - 2.58*2.3/sqrt(30)
L = 78 - 1.083395
L = 76.916605
L = 76.92


The upper value of the confidence interval is
U = xbar + z*sigma/sqrt(n)
U = 78 + 2.58*2.3/sqrt(30)
U = 78 + 1.083395
U = 79.083395
U = 79.08


The 99% confidence interval is therefore
76.92 < μ < 79.08

</font>