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13 October, 15:42

The Highway Safety Department wants to study the driving habits of individuals. A sample of 41 cars traveling on the highway revealed an average speed of 60 miles per hour and a standard deviation of 7 miles per hour. The population of car speeds is approximately normally distributed. Determine a 90% confidence interval estimate for the speed of all cars.

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  1. 13 October, 17:43
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    58,21 ≤ μ ≤ 61,79

    Step-by-step explanation:

    Normal Distribution

    Poputation size n = 41

    Population mean X = 60

    Population standard deviation σ = 7

    Question is: Confidence Interval 90 %?

    As Confidence Interval is 90 % then α = 10 %

    And as we are dealing with a two tail test

    α/2 = 0,05

    We look in Z table for values for α/2 = 0,05 and find

    z (α/2) = - 1,64 and z (α/2) = 1,64

    Then

    Confidence Interval is

    X - Zα/2 * σ/√n ≤ μ ≤ X + Zα/2 * σ/√n

    60 - (1,64) * 7/√41 ≤ μ ≤ 60 + (1,64) * 7/√41

    60 - 1,64 * 1,09375 ≤ μ ≤ 60 + 1,64 * 1,09375

    60 - 1,79375 ≤ μ ≤ 60 + 1,79375

    58,21 ≤ μ ≤ 61,79
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