Final answer:
To find the Z-score associated with a cumulative area of 0.12 on a TI-84 calculator, use the invNorm function by entering invNorm(0.12), and the calculator will display the Z-score rounded to two decimal places.
Step-by-step explanation:
To find the Z-score for which the area to its left is 0.12 using a TI-84 calculator, you should use the invNorm function. This function will give you the Z-score that corresponds to a given cumulative probability from the standard normal distribution. Since the area to the left is the cumulative probability, you would enter invNorm(0.12) to find the Z-score.
To do this on a TI-84 calculator, follow these steps:
- Press the '2nd' button, then 'VARS' to access the distribution menu.
- Scroll down to select '3:invNorm('. Alternatively, you can type '3' to select it directly.
- Enter the desired cumulative probability, which is 0.12 in this case, so you input '0.12'.
- Close the parentheses by typing ')' and press 'ENTER'.
The calculator will display the Z-score rounded to two decimal places. This Z-score is the number of standard deviations the value is from the mean in a standard normal distribution.