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Math Help - Normal Distribution, Std. Dev., & Probability

  1. #1
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    Smile Normal Distribution, Std. Dev., & Probability

    Suppose that a doorway being constructed is to be used by a class of people whose heights are normally distributed with a mean of 70 inches and a standard deviation of 3 inches.

    A) How high should the doorway be, without causing more than 25% of the people to bump their heads?

    B) If the height of the door is fixed at 76 inches, how many persons out of 5000 are expected to bump their heads?
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    Quote Originally Posted by ccdelia7 View Post
    Suppose that a doorway being constructed is to be used by a class of people whose heights are normally distributed with a mean of 70 inches and a standard deviation of 3 inches.

    A) How high should the doorway be, without causing more than 25% of the people to bump their heads?

    B) If the height of the door is fixed at 76 inches, how many persons out of 5000 are expected to bump their heads?
    A) Use the inverse normal idea to get the value of a such that Pr(X > a) = 0.25. This will give the minimum height of the door.

    B) Find p = Pr(X > 76). Multiply this number by 5000.

    The reason for this is that if Y is the random variable number of people who bump their head, then Y ~ Binomial(n = 5000, p). And you know E(Y) = np ......
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    sorry

    I'm sorry, but I simply have no idea where to start here! I have never taken a prob and stat course, and barely know what any of these terms mean! If you could go into more detail, that would be great!
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    Quote Originally Posted by ccdelia7 View Post
    I'm sorry, but I simply have no idea where to start here! I have never taken a prob and stat course, and barely know what any of these terms mean! If you could go into more detail, that would be great!
    I've shown you exactly what you need to calculate. They are routine calculations. I have no idea how you've been taught to do them (tables, technology such as TI-84, software etc) so there's not a lot more I can say except that your textbook or class notes will have examples of how to do these sorts of calculations.
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