Sometimes it is necessary to calculate the value of z (i.e z-score for a given probability). The applet below helps to calculate the z-score for any given probability. Drag the black slider back and forth to change the probability that you want to investigate.
Type the z-score that corresponds with a probability of the lower 75%.
No matter where you move the slider, what do you know about the relationship between the shaded left part of the graph and the unshaded right part of the graph?
Notice that the applet only calculates z-scores for probabilities below the value of [math]Z_a[/math]. How could you change your input to get the probability above the value of [math]Z_a[/math] (the unshaded part)?
Choose the z-score that corresponds with the probability of the upper 75%.
What do you notice about the answers for the questions about the lower 75% and the upper 75%?
Describe how you might try to calculate the z-scores that correspond with the [i]middle[/i] 75% of the distribution.