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Math Help - Determine Score

  1. #1
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    Determine Score

    I'm doing an on-line stats class and need some clarification.

    info as follows:

    mean=174.5centimeters
    standard deviation = 6.9centimeters

    What is the probability that 1 randomly selected person's height is greater than
    185centimeters?

    I calculated it as:

    z= 185-174.5 / 6.9

    z= 1.5

    Using Z-Score table I determined 1.5 = .9332 resulting in 1-.9332 = .0668

    So there is a 6.68% probability of 1 person's height being > 185centimeters.

    So far so good; however the follow on question ask to find two heights that seperate the top 25% and the bottom 20% of the population.

    Question 1: Using x = u + (z * standard deviation) for the top 25%, do I look up .25 on the table (-1.96) and solve for the top 25% height, because I get a number that is < the mean height of 174.5?

    x=174.5 + (-1.96 * 6.9) = 160.976

    Question 2: Is the process the same for the bottom 20%?

    Appreciate any suggestions.
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  2. #2
    hpe
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    Quote Originally Posted by sarugaki
    So far so good; however the follow on question ask to find two heights that seperate the top 25% and the bottom 20% of the population.

    Question 1: Using x = u + (z * standard deviation) for the top 25%, do I look up .25 on the table (-1.96) and solve for the top 25% height, because I get a number that is < the mean height of 174.5?
    You looked up 0.025 on your table. You need to look up 0.75 (!), because that would be the probability to the leftt of the desired height; 0.25 is to the right Then the rest bis OK.

    x=174.5 + (-1.96 * 6.9) = 160.976
    Question 2: Is the process the same for the bottom 20%?
    Yes, with a different z.
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