Understanding the Concept of the Area Under the Curve in Statistics and Normal Probability Distribution

The area under the curve of a normal probability distribution is always equal to 1

That statement is true

That statement is true. The area under the curve of a normal probability distribution is always equal to 1.

In a normal distribution, the curve is bell-shaped and symmetrical. The total area under the curve represents the total probability of all possible outcomes. Since the total probability of all possible outcomes must be equal to 1, the area under the curve is always 1.

This means that if you were to shade the entire area under the curve in a normal distribution, the shaded area would occupy exactly 100% of the total area.

The concept of the area under the curve is important in statistics because it allows us to determine probabilities of specific events or range of values occurring. By calculating the area under the curve between certain values or cutoff points, we can determine the probability of an event or value falling within that range.

For example, if we want to find the probability of a random variable falling between two values, we can calculate the area under the curve between those two values. Since the total area under the curve is 1, the calculated area will represent the probability of the event occurring.

So, in summary, the area under the curve of a normal probability distribution is always equal to 1 because it represents the total probability of all possible outcomes.

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