Normal distribution statistics question?

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  • 3 months ago

    a) We require P(x < 600) => P(z < (600 - 510)/107)

    i.e. P(z < 90/107) => P(z < 0.84)

    From normal tables we get:

    0.79955 => 80%

    b) We require P(x > 575) => P(z > (575 - 510)/107)

    i.e. P(z > 65/107) => P(z > 0.61)

    so, 1 - P(z < 0.61) => 1 - 0.72907

    or, 0.27093

    So, for a random sample of 1000 we have:

    0.27093 x 1000 => 271 score greater than 575

    :)>

  • Look up z-scores.

    (600 - 510) / 107 = z[1]

    90/107 = z[1]

    z[1] = 0.8411

    http://www.z-table.com/

    z = 0.8411 corresponds to 0.7995 of the graph being below that point, or 79.95%

    (575 - 510) / 107 = 65/107 = 0.6075 = (approximately) 0.61

    0.7291

    72.91% of the graph is below that point

    1000 * (1 - 0.7291) =>

    1000 * 0.2709 =>

    270.9 =>

    271

    You should expect to find 271 students out of 1000 who make a score greater than 575

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