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Thread: Simple problem, normal distribution

  1. #1
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    Simple problem, normal distribution

    How would you answer this? Police have proved 45% of people the give speeding tickets to are aged between 18-25. If they pull over 8 people what is the probability that 6 are aged 18-25?

    Thank you!!
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  2. #2
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    Re: Simple problem, normal distribution

    Quote Originally Posted by ictodd View Post
    How would you answer this? Police have proved 45% of people the give speeding tickets to are aged between 18-25. If they pull over 8 people what is the probability that 6 are aged 18-25?

    Thank you!!
    This is not a normal distribution problem but a binomial distribution problem. Number r of people in a sample of N in the age bracket is:

    $\displaystyle b(r;N,0.45)=\frac{N!}{(N-r)!r!}(0.45)^r(0.55)^{N-r}$

    The sample size would have to be much larger than 8 for the use of the normal approximation to be valid, though the binomial calc gives a probability of 6.88% and the normal in this case 7.03%.

    If you want to try the normal approximation calculation start by calculating the mean and standard deviation $\displaystyle \mu,\ \sigma$ of the number of people in the given age group pulled over. Then you need to compute the probability using the normal distribution $\displaystyle N(\mu, \sigma^2)$ of between $\displaystyle 5.5$ and $\displaystyle 6.5$.


    CB
    Last edited by CaptainBlack; Nov 12th 2011 at 11:49 PM.
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