1. What is the Normal Distribution Critical Value?

The critical value in a normal distribution is a point on the distribution that is compared to a test statistic to determine whether to reject the null hypothesis. It represents the threshold for statistical significance.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \mu \) — Mean of the distribution
• \( Z \) — Z-score (standard score)
• \( \sigma \) — Standard deviation of the distribution

Explanation: The critical value is calculated by adding the product of the Z-score and standard deviation to the mean of the distribution.

3. Importance of Critical Value Calculation

Details: Critical values are essential in hypothesis testing, confidence interval construction, and determining statistical significance in research studies.

4. Using the Calculator

Tips: Enter the mean, Z-score (which can be positive or negative), and standard deviation (must be positive). The calculator will compute the critical value.

5. Frequently Asked Questions (FAQ)

Q1: What is a Z-score?
A: A Z-score measures how many standard deviations an element is from the mean. Positive Z-scores are above the mean, negative are below.

Q2: How do I find the Z-score for a given confidence level?
A: Common Z-scores: 1.96 for 95% confidence, 2.576 for 99% confidence. Use Z-tables or inverse normal calculators for other values.

Q3: Can the standard deviation be zero?
A: No, the standard deviation must be greater than zero for this calculation to be meaningful.

Q4: What's the difference between critical value and p-value?
A: Critical value is a threshold on the distribution, while p-value is the probability of observing a test statistic as extreme as the one calculated.

Q5: When would I need a two-tailed critical value?
A: For two-tailed tests, you need both positive and negative critical values at the appropriate significance level (e.g., ±1.96 for 95% confidence).