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11 January, 17:34

Suppose a certain population of observations is normally distributed. What percentage of the observations in the population.

(a) are within + 1.5 standard deviations of the mean?

(b) are more that 2.5 standard deviations above the mean?

(c) are more that 3.5 standard deviations away from (above or below) the mean?

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  1. 11 January, 19:01
    0
    For the standard normal distribution Z, the mean μ = 0

    and σ the standard deviation = 1

    a) P (0 ≤ Z ≤ 1.5) →P (Z=1.5) - P (Z=0)

    P (0 ≤ Z ≤ 1.5) = 0.9332 - 0.5 = 0.4322

    b) P (Z ≥ 2.5) →P (Z=2.5) = 1 - P (Z=2.5)

    P (Z ≥ 2.5) = 1 - 0.9938 = 0.0062

    c) P (Z≥ 3.5) = 1 - P (Z = 3.5) = 0

    OR P (Z≤ 3.5) = 0
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