If Z Is a Standard Normal Random Variable, Find the Value

question 14

Short Answer

If Z is a standard normal random variable, find the value of z that has the following probabilities:
a. $\mathrm { P } ( Z \leq z ) = 0.3228$
b. $\mathrm { P } ( Z \geq z ) = 0.8289$

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Definitions:

Normally Distributed

Describes a statistical distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Gasoline Prices

The cost per unit of gasoline, which can fluctuate based on factors such as crude oil prices, supply and demand, taxes, and market speculation.

Standard Normal Distribution

A normal distribution with a mean of zero and a standard deviation of one, used in many statistical methods.

Z-axis

The axis in a three-dimensional coordinate system representing the depth, perpendicular to both the X-axis (horizontal) and Y-axis (vertical).