Exam scores in a MATH 1030 class is approximately normally distributed with mean 87 and standard deviation 5.8. Round answers..?

Exam scores in a MATH 1030 class is approximately normally distributed with mean 87 and standard deviation 5.8. Round answers to the nearest tenth of a percent.

a) What percentage of scores will be less than 92?

b) What percentage of scores will be more than 85?

c) What percentage of scores will be between 83 and 89?

3 Answers

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

    Find the z-scores for each:

    a) (92 - 87) / 5.8

    5 / 5.8

    25/29

    0.86206896551724137931034482758621

    z = 0.86, p = 0.8051

    80.51%

    b)

    (85 - 87) / 5.8 =>

    -2/5.8 =>

    -10/29 =>

    -0.34482758620689655172413793103448

    1 - z(-0.34) =>

    1 - 0.3669 =>

    0.6331

    63.31%

    c)

    (83 - 87) / 5.8 =>

    -4/5.8 =>

    -20/29

    (89 - 87) / 5.8 =>

    2/5.8 =>

    10/29

    z(10/29) - z(-20/29) =>

    z(0.344) - z(-0.690) =>

    0.6331 - 0.2451 =>

    0.3880

    38.8%

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  • Anonymous
    6 months ago

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  • 6 months ago

    (a) z = (92 - 87)/5.8 = 0.86207;

    normal distribution table says 80.6% of scores are less than this.

    (b) z = (85 - 87)/5.8 = -0.34483;

    normal distribution table says 13.5% of scores are between z=0 and z=-0.345;

    therefore 63.5% of scores are higher than z = -0.345.

    (c) z1 = (83 - 87)/5.8 = -0.68966 and

    z2 = (89 - 87)/5.8 = +0.34483;

    normal distribution table says 13.5% of scores are between z = 0 and z2,

    while 25.5% of scores are between z1 and z=0;

    therefore 49.0% of scores are between z1 and z2.

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