Meaning of “statistics table A”
Common convention: In many introductory statistics textbooks, statistics table A is the standard normal table (also called the Z table). It reports the cumulative probability \(P(Z \le z)\) for a standard normal random variable \(Z \sim N(0,1)\).
What values the table provides
The Z table (Table A) typically provides the area (probability) to the left of a z-score:
\[ \text{Table A entry at } z \text{ equals } P(Z \le z). \]
How to use Table A step by step
- Standardize a normal value \(x\) to a z-score when needed: \[ z=\frac{x-\mu}{\sigma}. \] If the problem already gives a z-score, this step is skipped.
-
Locate \(z\) in the table. Most Table A layouts use:
- the left margin for the first decimal place (e.g., \(1.2\)),
- the top row for the second decimal place (e.g., \(0.03\)),
- the intersection cell for \(P(Z \le 1.23)\).
-
Convert to the probability requested using complements and differences:
- Right tail: \[ P(Z>z)=1-P(Z\le z). \]
-
Between two z-scores \(a
- Negative z-scores (symmetry): \[ P(Z\le -z)=1-P(Z\le z)\quad (z>0). \]
Small excerpt illustrating a “Table A” layout
The table below is a compact excerpt for \(P(Z\le z)\) near \(z=1.20\) to \(z=1.25\), shown only to demonstrate how the row/column lookup works.
| Row (z) | +0.00 | +0.01 | +0.02 | +0.03 | +0.04 | +0.05 |
|---|---|---|---|---|---|---|
| \(1.2\) | \(0.8849\) | \(0.8869\) | \(0.8888\) | \(0.8907\) | \(0.8925\) | \(0.8944\) |
Worked example using “statistics table A”
Suppose Table A is used to find \(P(Z>1.23)\). The excerpt shows \(P(Z\le 1.23)\approx 0.8907\). Then:
\[ P(Z>1.23)=1-P(Z\le 1.23)\approx 1-0.8907=0.1093. \]
Visualization: left-tail area \(P(Z\le z)\) represented by Table A
Summary
“Statistics table A” most often refers to the standard normal (Z) table giving \(P(Z\le z)\). Row/column lookup provides the left-tail area, and complements or differences convert that value to right-tail and between-probabilities.