In the following problems the
normalized score is z = (x – μ)/σ,
where μ is
the mean and σ is
the standard deviation; that is, z = (x – 22.1)/2.3

17. P(20
≤
x ≤ 24) = P(-0.9130 ≤
z ≤ 0.8261) = 0.6150 or 61.5% (the probability of choosing a student from a given set is equal to the percentage of the students in the set).

18. P(23
< x) = P(0.3913
< z) = 0.3477 or
34.8%

19. P(20.5
< x) =P(-0.6957 <
z) = 0.7567 or 75.7%

20. P(x
< 25.5) = P( z < 1.4783) = 0.9303 or 93.0%

Apr 27th, 2015

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