Question 983356
A local Board of Elections wants to estimate the average number of voters per district for the last election. A random sample of 81 districts shows a sample mean of 168 voters with a standard deviation of 45 voters. Find a 99% confidence interval (to the nearest tenth) for the population mean number of voters per district. 

Solution:
 Central Limit Theorem applies because the sample size, n > 30
R code:
> n = 81
> s = 45
> SE = s/sqrt(n)
> E = qnorm(.995)*SE  #margin of error
> xbar =168
> xbar + c(-E, E)
[1] 155.1209 180.8791

The 99% confidence interval for the population mean number of voters per district to the nearest tenth is (155.1, 180.9)

Interpretation:
99% of all samples of size 81 will contain the unknown population mean number of voters per district (μ) between its lower and upper confidence interval limits.