Standard Normal Area
1. The problem is to understand the Standard Normal Distribution Table that shows the area from 0 to $z$.
2. The Standard Normal Distribution is a normal distribution with mean 0 and standard deviation 1.
3. The table you provided gives the cumulative area under the curve from 0 to a positive $z$-score, where $z$ values range from 0 to 3 in increments of 0.01.
4. For example, to find the area from 0 to $z=1.23$, locate the row for 1.2 and the column for 0.03, which gives the value 0.3907.
5. This means the probability that a standard normal random variable falls between 0 and 1.23 is approximately 0.3907.
6. This table is useful to find probabilities and critical values in problems involving the standard normal distribution.
7. Always remember the total area under the whole standard normal curve is 1, with an area of 0.5 to the left and 0.5 to the right of the mean 0.
Final understanding: The table helps us find $P(0 < Z \le z)$ for various positive values of $z$ in a clear and organized way.