Use the ti 84 calculator to find the z score for which the area to the right is 0.09
The Correct Answer and Explanation is :
To find the z-score for which the area to the right is 0.09 using the TI-84 calculator, you can follow these steps:
Steps to Find the Z-Score:
- Turn on the calculator and press the 2nd button, then press the VARS button to access the distribution menu.
- Scroll down to option 3: invNorm and press ENTER.
- The prompt will ask for the area to the left. Since we are given the area to the right (0.09), we need to find the area to the left, which is 1 – 0.09 = 0.91.
- Enter 0.91 as the area to the left.
- For the mean and standard deviation, the default values of 0 for the mean and 1 for the standard deviation (assuming a standard normal distribution) should be used.
- Press ENTER, and the calculator will display the corresponding z-score.
The z-score you get will be approximately 1.34.
Explanation:
The z-score represents the number of standard deviations a data point is from the mean. In a normal distribution, the area to the right of a z-score corresponds to the proportion of the distribution that lies above that score. Since the area to the right is given as 0.09, we know that 9% of the distribution lies above this z-score.
To find the z-score corresponding to an area to the right of 0.09, we first convert this to an area to the left, which is 1 – 0.09 = 0.91. This means that the z-score will correspond to the point where 91% of the data lies below it.
Using the invNorm function on the TI-84, we input the area to the left (0.91) and use the default mean (0) and standard deviation (1) for a standard normal distribution. The TI-84 calculator uses the inverse cumulative normal distribution to give us the z-score that matches the area.
This process is essential in statistical analysis to standardize values and make them comparable across different datasets or distributions. By knowing the z-score, you can interpret how far a specific data point is from the mean and understand the probability of values occurring below or above it.
Let me generate an image that shows the TI-84 calculator’s screen with the result.
Here is an image of the TI-84 calculator screen showing the z-score calculation for an area to the right of 0.09. The screen displays the invNorm(0.91, 0, 1) function and the result of approximately 1.34, with the standard normal distribution graph illustrating the area to the right.
