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    On a test by 100 students, the average mark is 65, with variance 144. student A scores 83, student B scores 47
    a) calculate the z-scores for these two students
    b) what is the maximum number of students with a score either better than A's or worse than B's
    c) what is the maximum number of students with a score better than A's? (using chebyshev's inequality theory)


    Can anyone help me on this ? desparately. Rest assured rep will be awarded.
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    z-scores? Is that the normal distribution?
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    I guess you could assume test scores to be in a normal distribution.
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    yes normal distribution
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    (Original post by iceman_jondoe)
    On a test by 100 students, the average mark is 65, with variance 144. student A scores 83, student B scores 47
    a) calculate the z-scores for these two students
    Assuming the marks are distributed normally then, let X be the DRV 'marks obtained in test' then,

    X ~ N(65, 12²)
    P(X » 83) = (83-65)/12 = 1.5
    P(X « 47) = (47-65)/12 = -1.5
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    (Original post by iceman_jondoe)
    On a test by 100 students, the average mark is 65, with variance 144. student A scores 83, student B scores 47
    b) what is the maximum number of students with a score either better than A's or worse than B's
    b)P(X>83) = P(Z>[83-65]/12)
    = P(Z>1.5)
    = 1 - 0.9332
    = 0.0668
    p(X<47) = P(Z<[47-65]/12)
    = P(Z<-1.5)
    = 0.0668
    P(score either better than A's or worse than B's)
    = 0.0668 + 0.0668
    =0.1336

    Therefore, the maximum number of students with a score either better than A's or worse than B's
    = 0.1336 . 100 (Since there are 100 students)
    = 13.36
    = 13 students

    Is it right or wrong? And sorry I've never heard of chebyshev's inequality theory. But I just do it in this way...

    c)the maximum number of students with a score better than A's
    = 0.0668 . 100
    = 6.68
    = 7 students
 
 
 
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