If P(Z greater than z) = 0.67, then z = -0.44. True False

Question:

If P(Z > z) = 0.67, then z = -0.44.

True

False

Standard Score:

Standard scores (usually written as z scores) are number of standard deviations random variables takes below or above the mean in a continuous distribution.

Answer and Explanation:

It is TRUE.

If probability of getting a Z greater than z is greater than 0.5, the z must be negative. Using z table;

{eq}\begin{align*} P(Z>z)&=1-P(Z\le z)\\0.67&=1-P(z\le z)\\0.33&=P(Z\le z)\\z&=z_{0.33}\\z&=-0.44 \end{align*} {/eq}


Learn more about this topic:

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Estimating Areas Under the Normal Curve Using Z-Scores

from Statistics 101: Principles of Statistics

Chapter 6 / Lesson 7
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