# Studying for a simple Stats test. What does P mean and how do I solve this for a z-score. P(z<1.37). My table in our book is different?

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#### Explanation

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'P' is short for "probability".

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Without going too far into the details of probability theory, **events**, or subsets of a sample space, and maps them to numbers between 0 and 1 (similar to how

Quick example: let *event* that a single coin toss lands heads-up. Then the probability of

Sample space

#S={"H","T"}#

Subset#E={"H"}#

#"P"(E)=("size of "E)/("size of "S)=1/2.#

Elements of a sample space can be encoded into **random variables.** To do this, we just map each element of the sample space to a number. In the coin toss example, we could map "heads" to

#"P"(X=1)=1/2.#

*The probability of "event #E# occurring" is the same as the probability of "#X# being equal to 1".*

Skipping a few chapters in statistics, there are many special types of random variables that have useful **distributions**, or patterns in how they map events to numbers. One such common random variable is called **standard normal distribution**. Ever hear of a bell curve? Well,

*any* normal random variable

#"P"(X < x)="P"(Z<(x-mu)/sigma)#

That's why we have

Alright, enough background. You need to know how to find *area* under the **there are two ways a table may choose to do this.** It may show you:

- the probability of
#Z# beingless than#z# (lower-tail)- the probability of
#Z# beinggreater than#z# (upper-tail)

It is up to you to know how to interpret the matching probability for your

If we want **the total area under any random variable's distribution curve is always 1.** Meaning:

#"P"(Z < z)" "+" ""P"(Z > z)" "=" "1#

or

#"P"(Z < z)" "=" "1" "-" ""P"(Z > z)#

So for example, if you look up *left* of that

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