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To estimate the mean height population of male students on your campus, you will measure and SRS of students. Heights of people the same sex and similiar ages are close to normal. You know from government data that the standard deviation of the heights of young men is about 2.8 inches. Suppose (that unknown to you) the mean heights of all males students is 70 inches.

A. If you choose one student at random, what is the probability that he is between 69 and 78 inches tall?

B. You measure 25 students. What is the sampling distribution of their average height X (sample mean)?

C. What is the probability that the mean height of your sample is between 69 and 71 inches?

I missed my class, and I'm lost on how to do this.

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  1. A. Z = (score-mean)/SD

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

    B. Stand Error of the mean (SEm) = SD/√(n-1)

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

    SEdiff = √(SEmean1^2 + SEmean2^2)

    SEm = SD/√(n-1)

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

    Use that same table.

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