A group of students at a school takes a history test. The distribution is normal with a mean of 25,

Discussion in 'Calculator Requests' started by math_celebrity, Jan 5, 2017.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    A group of students at a school takes a history test. The distribution is normal with a mean of 25, and a standard deviation of 4.

    (a) Everyone who scores in the top 30% of the distribution gets a certificate.
    (b) The top 5% of the scores get to compete in a statewide history contest. What is the lowest score someone can get and still go onto compete with the rest of the state?

    (a) Top 30% is 70% percentile
    Inverse of normal distribution(0.7) = -0.5244005
    Plug into z-score formula, -0.5244005 = (x - 25)/4
    x = 22.9024

    (b) Top 5% is 95% percentile
    Inverse of normal distribution(0.95) = 1.644853627
    Plug into z-score formula, 1.644853627 = (x - 25)/4
    x = 31.57941451
     

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