Calculate the Following Probabilities Using the Standard Normal Distribution $\operatorname { Pr } ( Z < 0.0 )$

question 42

Essay

Calculate the following probabilities using the standard normal distribution.Sketch the
probability distribution in each case, shading in the area of the calculated probability. (a) $\operatorname { Pr } ( Z < 0.0 )$
(b) $\operatorname { Pr } ( Z \leq 1.0 )$
(c) $\operatorname { Pr } ( Z > 1.96 )$
(d) $\operatorname { Pr } ( Z < - 2.0 )$
(e) $\operatorname { Pr } ( Z > 1.645 )$
(f) $\operatorname { Pr } ( Z > - 1.645 )$
(g) $\operatorname { Pr } ( - 1.96 < Z < 1.96 )$
(h) $\operatorname { Pr } ( Z < 2.576$ or $Z > 2.576 )$
(i) $\operatorname { Pr } ( Z > z ) = 0.10$ ; find $z$ .
(j) $\operatorname { Pr } ( Z < - z$ or $Z > z ) = 0.05$ ; find $z$ .

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Definitions:

Central Nervous System

consists of the brain and spinal cord, serving as the primary processing center for the entire nervous system and coordinating all bodily functions.

Coordination

The ability to use different parts of the body together smoothly and efficiently.

Central Nervous System

Comprises the brain and spinal cord, functioning as the primary control center for processing and transmitting information throughout the body.

Autonomic System

A part of the nervous system that controls involuntary bodily functions such as heart rate, digestion, and respiratory rate.