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Math Help - Confidence interval

  1. #1
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    Confidence interval

    Find a 95% confidence interval for the percentage of cars on a certain highway that have poorly adjusted brakes, using a random sample of 500 cars stopped at a roadblock on that highway, 87 of which had poorly adjusted brakes.

    I think I need to find k, with

    k = \frac{cs}{\sqrt n}

    n = 500, \mu = 87.

    Not sure how to find c or s.
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  2. #2
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    Re: Confidence interval

    Try this

    \frac{87}{500}\pm 1.96\times \sqrt{\frac{\frac{87}{500}\left(1-\frac{87}{500}\right)}{500}}
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  3. #3
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    Re: Confidence interval

    Quote Originally Posted by pickslides View Post
    Try this

    \frac{87}{500}\pm 1.96\times \sqrt{\frac{\frac{87}{500}\left(1-\frac{87}{500}\right)}{500}}
    Where did that come from? When I calculated it I got .5063 and -0.1583.


    This is the answer, but I don't know how c or s^2 was calculated.

    For c, I tried .5(1+.95) = .975 and looking up the value for .975 on the t distribution chart with 50 - 1 = 49 degrees of freedom. But 49 was not on the chart.

    For s^2, I'm not understanding why it is 87 * 413 / 500.
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