The 98% confidence interval for the mean gas mileage for this car model is (26.07,30.73).
Confidence intervals are defined as a range of values with a known chance that a parameter's value falls inside them.
The confidence interval of statistical data is computed using the formula:
[tex](\overline{x} - Z\frac{\sigma }{n},\overline{x} + Z\frac{\sigma }{n})[/tex]
where [tex]\overline{x}[/tex] is the mean, Z is the Z-score corresponding to the confidence interval, σ is the standard deviation, and n is the sample size.
In the question, the sample size (n) = 36, the mean of the sample ([tex]\overline{x}[/tex]) = 28.4 mi/gallon, the standard deviation (σ) = 6 mi/gallon.
The confidence interval given to us is 98%.
Z-score corresponding to this (Z) = 2.33.
Thus, the confidence interval can be calculated as:
(28.4 - 2.33{6/√36},28.4 + 2.33{6/√36})
= (28.4 - 2.33,28.4 + 2.33)
= (26.07,30.73).
Thus, the 98% confidence interval for the mean gas mileage for this car model is (26.07,30.73).
Learn more about constructing confidence intervals at
https://brainly.com/question/17030704
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