1. What is the Standard Normal Curve Between Calculator?

The Standard Normal Curve Between Calculator calculates the probability between two z-scores in a standard normal distribution. It determines the area under the curve between two specified z-values, which represents the probability that a randomly selected value falls between those two points.

2. How Does the Calculator Work?

The calculator uses the standard normal distribution formula:

Where:

• \( \Phi(z) \) — Cumulative Distribution Function (CDF) of the standard normal distribution
• \( z_1 \) — First z-score
• \( z_2 \) — Second z-score

Explanation: The calculator finds the area under the standard normal curve between two z-scores by calculating the difference between their cumulative probabilities.

3. Importance of Z-Score Calculation

Details: Calculating probabilities between z-scores is fundamental in statistics for determining likelihoods, confidence intervals, hypothesis testing, and understanding data distribution in standardized terms.

4. Using the Calculator

Tips: Enter two z-scores (can be positive or negative values). The calculator will compute the probability that a value falls between these two points in a standard normal distribution.

5. Frequently Asked Questions (FAQ)

Q1: What is a z-score?
A: A z-score measures how many standard deviations a data point is from the mean of a distribution.

Q2: What is the range of possible probabilities?
A: Probabilities range from 0 to 1, where 0 indicates impossibility and 1 indicates certainty.

Q3: Can z-scores be negative?
A: Yes, negative z-scores indicate values below the mean, while positive z-scores indicate values above the mean.

Q4: What if I enter z1 greater than z2?
A: The calculator will return a negative probability, which indicates that z1 is greater than z2. For meaningful results, ensure z1 ≤ z2.

Q5: How accurate is the calculation?
A: The calculation uses a well-established approximation of the normal CDF with high accuracy for most practical purposes.