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:

Frequency

In general terms, the rate at which something occurs over a particular period of time or in a given sample.

Actor-observer Bias

A cognitive bias that affects the way we attribute causes to our own behaviors versus those of others, often attributing our own actions to situational factors while attributing others' actions to their personality or character.

Self-serving Bias

Self-serving bias is a common cognitive bias that leads individuals to attribute their successes to internal factors while attributing failures to external factors, protecting self-esteem.

Recency Effect

The phenomenon of better remembering the most recent information presented in a series of data or events.