1. What is a Right-Tailed Z-Score?

The right-tailed Z-score (Z) is the inverse normal distribution value corresponding to a given probability (p) in the right tail of the standard normal distribution. It represents how many standard deviations a point is from the mean for a given right-tail probability.

2. How Does the Calculator Work?

The calculator uses the inverse normal distribution function:

Where:

• \( Z \) — Standard normal deviate (Z-score)
• \( \Phi^{-1} \) — Inverse standard normal cumulative distribution function
• \( p \) — Right-tailed probability (0 to 1)

Explanation: The function calculates the Z-score that corresponds to the (1-p) percentile of the standard normal distribution.

3. Importance of Z-Score Calculation

Details: Right-tailed Z-scores are crucial in hypothesis testing, confidence intervals, and determining statistical significance in right-tailed tests.

4. Using the Calculator

Tips: Enter a probability value between 0 and 1. The calculator will return the corresponding Z-score for the right tail of the standard normal distribution.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between left and right-tailed Z-scores?
A: Left-tailed Z-scores correspond to cumulative probabilities, while right-tailed Z-scores correspond to 1 minus the cumulative probability.

Q2: What are common Z-score values used in statistics?
A: Common right-tailed Z-scores: 1.96 (p=0.025), 2.326 (p=0.01), 2.576 (p=0.005) for 95%, 99%, and 99.5% confidence levels respectively.

Q3: How is this related to p-values?
A: The right-tailed Z-score can be converted to a p-value by calculating 1 minus the cumulative distribution function at that Z-score.

Q4: What if I need a two-tailed Z-score?
A: For two-tailed tests, use half your desired alpha level (e.g., for α=0.05, use p=0.025).

Q5: When would I use this in real-world applications?
A: Commonly used in quality control, medical testing, and any scenario where you need to determine if a value is significantly higher than expected.