Answer to Question #215121 in Statistics and Probability for lex

Question

James kept careful records of the fuel efficiency of his car. After the first 100 times he filled up the tank, he found the mean was 23.4 miles per gallon (mpg) with a population standard deviation of 0.9mpg. Compute the 95 percent confidence interval for his mpg.

Answer 1

$\mu=23.4 \\ \sigma=0.9 \\ n=100$

Two-sided confidence interval:

$CI = (\mu - \frac{Z_c \times \sigma}{\sqrt{n}}, \mu + \frac{Z_c \times \sigma}{\sqrt{n}}) \\ CI = (23.4 - \frac{1.96 \times 0.9}{\sqrt{100}}, 23.4 + \frac{1.96 \times 0.9}{\sqrt{100}}) \\ CI = (23.4 - 0.176, 23.4 + 0.176) \\ CI = (23.224, 23.576)$