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27 December, 19:01

For a standard normal distribution, which of the following expressions must always be equal to 1?

A) P (z≤-a) - P (-a≤z≤a) + P (z≥a)

B) P (z≤-a) - P (-a≤z≤a) + P (z≥a)

C) P (z≤-a) + P (-a≤z≤a) - P (z≥a)

D) P (z≤-a) + P (-a≤z≤a) + P (Z≥a)

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  1. 27 December, 20:53
    0
    P (z ≤ - a) + P (-a ≤ z ≤ a) + P (z ≥ a) = 1 - P (z ≤ a) + [P (z ≤ a) - P (z ≤ - a) ] + 1 - P (z ≤ a) = 2 - 2P (z ≤ a) + P (z ≤ a) - [1 - P (z ≤ a) ] = 2 - P (z ≤ a) - 1 + P (z ≤ a) = 1

    Therefore, option D is the correct answer.
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