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    ​The distribution of heights (in inches) of students aged 18–20 has a mean of 54 and standard deviation of 2.5. What will be the z-score for a student
    Question

    The distribution of heights (in inches) of students aged 18–20 has a mean of 54 and standard deviation of 2.5. What will be the z-score for a student who is 5 feet tall?

    A.

    2.4

    B.

    3.1

    C.

    1.5

    D.

    2.9

    Correct option is A

    Explanation-

    To calculate the z-score, we use the formula:

    z=Xμσz = \frac{X - \mu}{\sigma}

    Where:
     = the observed value (in this case, 5 feet = 60 inches)
     = the mean (average) = 54 inches
     = the standard deviation = 2.5 inches

    by putting the values-

    z=60542.5=62.5=2.4z = \frac{60 - 54}{2.5} = \frac{6}{2.5} = 2.4

    So, the correct answer is option A : 2.4


    ​​

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