A sample of 36 females is taken. What is the probability that the mean height of these women is shorter than 64 inches if we know the height for all American females is N(63,3^2)?
What is the probability that a random woman is shorter than 64 inches?

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  1. Z = (mean1 - mean2)/standard error (SE) of difference between means

    SEdiff = √(SEmean1^2 + SEmean2^2)

    SEm = SD/√(n-1) or just √n

    If only one SD is provided, you can use just that to determine SEdiff.

    Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.

    For the random woman:

    Z = (score-mean)/SD

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