Question

gasoline use a random sample of 64 drivers used on average 744 gallons of gasoline per year. the standard deviation of the population is 35 gallons.
part: 0 / 2
part 1 of 2
(a) find the 99% confidence interval of the mean for all drivers. round intermediate answers to at least three decimal places. round your final answers to the nearest whole number.
□ < μ < □

Explanation:

Step1: Identify key values

Sample size $n=64$, sample mean $\bar{x}=744$, population standard deviation $\sigma=35$, confidence level 99%.

Step2: Find z-score for 99% confidence

Two-tailed z-score $z_{0.005}=2.576$ (from standard normal table).

Step3: Calculate standard error

Standard error $SE=\frac{\sigma}{\sqrt{n}}=\frac{35}{\sqrt{64}}=4.375$.

Step4: Compute margin of error

Margin of error $E=z\times SE=2.576\times4.375\approx11.27$.

Step5: Find confidence interval

Lower bound: $\bar{x}-E=744-11.27\approx733$; Upper bound: $\bar{x}+E=744+11.27\approx755$.

Answer:

733 < μ < 755