What does the area corresponding to the critical value zcrt mean?
There is a graph that has a normal bell shape curve that has a vertical arrow that intersects the x axis far from the y axis. then everything to the left of the the vertical arrow is colored in blue. The question is asking what is that area? is it -p or the area that corresponds to the critical value crt?
In statistics, the area corresponding to the critical value, often denoted as z_crt, is the probability associated with a specific value or range of values on a normal distribution curve.
In your description of the graph, the vertical arrow intersects the x-axis at a point that is "far from the y-axis." This implies that the arrow is pointing to a value that represents the critical value, or z_crt.
The area to the left of the vertical arrow, which is colored in blue on the graph, represents the cumulative probability up until the critical value. It is important to note that this area corresponds to the probability associated with values lower than or equal to the critical value, not a specific numerical value.
To calculate the specific area or probability corresponding to the critical value z_crt, you would have to consult a standard normal distribution table or use statistical software. These resources provide the cumulative probabilities or areas under the curve for various z-scores.
So, to summarize, the area corresponding to the critical value z_crt represents the cumulative probability up until that specific value on the normal distribution curve.