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21 December, 06:40

The gas mileage for a certain model of car is known to have a standard deviation of 6 mi/gallon. A simple random sample of 64 cars of this model is chosen and found to have a mean gas mileage of 27.5 mi/gallon. Construct a 97.5% confidence interval for the mean gas mileage for this car model.

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  1. 21 December, 06:58
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    Answer: confidence interval = 27.5 + / - 1.68

    = (25.82, 29.18)

    Step-by-step explanation:

    Given;

    Number of samples n = 64

    Standard deviation r = 6mi/gallon

    Mean x = 27.5mi/gallon

    Confidence interval of 97.5%

    Z' = t (0.0125) = 2.24

    Confidence interval = x + / - Z' (r/√n)

    = 27.5 + / - 2.24 (6/√64)

    = 27.5 + / - 1.68

    = (25.82, 29.18)
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