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Math Help - 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:

    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 \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 N(\mu, \sigma^2) of between 5.5 and 6.5.


    CB
    Last edited by CaptainBlack; November 13th 2011 at 12:49 AM.
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