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March 29, 2017

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The distribution of scores is normal with a ì = 100 and ó =15. What proportion of the population have scores A) Above 130? B) Below 90? C) Above 110?

  • statistics - ,

    Given μ=100; σ=15.

    Standardize the distribution by
    z(x,μ,σ*sup2;)=(x-μ)/σ
    For example,
    (a)
    z(130,100,15^2)=(130-100)/15=2
    Use a normal distribution table to find
    P(z<2)=0.9772
    P(z>2)=1-0.9772=0.0228
    P(x>130)=P(z>2)=0.0228

    (b)
    z=(90-100)/15=-2/3
    P(x<90)=
    =P(z<-2/3)
    =P(z>2/3)
    =1-P(z<2/3)
    =1-0.7475
    =0.2525

    (c)
    P(x>110)
    can be found similar to (a)

    Many normal distribution tables are available online, such as:
    http://www.math.unb.ca/~knight/utility/NormTble.htm

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