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Math Help - (Intro Stats) Standard Normal Distribution

  1. #1
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    (Intro Stats) Standard Normal Distribution

    Can someone help me with this question?

    The average age of doctors in a certain hospital is 43.0 years old. Suppose the distribution of ages is normal and has a standard deviation of 8.0 years. If 25 doctors are chosen at random for a committee, find the probability that the average age of those doctors is less than 43.8 years. Assume that the variable is normally distributed.
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  2. #2
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    Re: (Intro Stats) Standard Normal Distribution

    Let Y = (X_1 + X_2 + ... + X_{25})/25 be the average age of 25 doctors where X_i is the age of a randomly selected doctor. If X_i is normally distributed then so is Y.

    Y will be distributed as follows: Y \sim N\left(43, \left(\frac{8}{\sqrt{25}}\right)^2 \right) (mean, variance)
    Last edited by Ridley; March 24th 2012 at 11:16 PM.
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