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Math Help - Standard Deviation with Mean w. binomial problem who will win a race

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    Exclamation Standard Deviation with Mean w. binomial problem who will win a race

    mark runs a fouty yard dash in 5.1 w. a standard deviation of .2 seconds
    Killio runs it in 5.0 seconds with a standard deviation of .15 seconds. if they race five times what is the probability that mark will win 4 times?
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    Quote Originally Posted by Statisticsperson View Post
    mark runs a fouty yard dash in 5.1 w. a standard deviation of .2 seconds
    Killio runs it in 5.0 seconds with a standard deviation of .15 seconds. if they race five times what is the probability that mark will win 4 times?
    Let X = M - K where M ~ Normal (\mu_M = 5.1, \sigma_M = 0.2) and K ~ Normal (\mu_K = 5.0, \sigma_K = 0.15). Then X follows a normal distribution whose mean and standard deviation can be calculated from here: Normal Difference Distribution -- from Wolfram MathWorld

    Calculate p = Pr(X) < 0.

    Let Y be the random variable number of times Mark wins. Then Y ~ Binomial(n = 5, p = as calculated above). Calculate Pr(Y = 4).
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