The fuel economy of a 2011 Lexus RX 350 using premium fuel i

The fuel economy of a 2011 Lexus RX 350 using premium fuel is normally distributed with a known population standard deviation of 1.25 mpg. If a random sample of 30 tanks of gas yields a mean of 21.0 mpg, find a 95% confidence interval for the true mean mpg (source: www.fueleconomy.gov). The upper and lower limits for the confidence interval are

Solution

Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

So the lower bound is

xbar - Z*s/vn =21 -1.96*1.25/sqrt(30)=20.55269

So the upper bound is

xbar + Z*s/vn=21 +1.96*1.25/sqrt(30)=21.44731