This calculator finds the area under the normal distribution curve for a specified mean, standard deviation, and range defined by lower and upper bounds. It helps in determining the probability that a random variable falls within this range, which is useful in various statistical applications.

**Area (P(lower ≤ X ≤ upper)):**

## Understanding the Normal Distribution

The **Normal Distribution** is a continuous probability distribution defined by its mean (μ) and standard deviation (σ).
It is widely used in statistics because of its well-known properties, such as symmetry and the 68-95-99.7 rule, which states that approximately
68% of the data falls within one standard deviation, 95% within two, and 99.7% within three.

### Key Parameters

**Mean (μ):**The center or peak of the distribution.**Standard Deviation (σ):**Measures the spread or dispersion of the distribution around the mean.**Lower and Upper Bounds:**Defines the range for calculating the area under the curve, representing the cumulative probability within this range.

### Using the CDF

The Cumulative Distribution Function (CDF) helps calculate the probability that a random variable X is less than or equal to a specified value. By setting lower and upper bounds, you can find the probability of X lying between these values.

Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, he’s focused on bringing more fun and curiosity to the world of science and research online.