The total area under the normal distribution curve is equal to a probability of
1
that's what defines a probability distribution
1. The total area under the normal distribution curve is equal to a probability of 1.
The normal distribution is a continuous probability distribution that is symmetrical and bell-shaped. The total area under the normal curve represents the total probability for all possible values of a random variable.
Since probability is always bound between 0 and 1, the total area under the normal distribution curve adds up to 1. This means that the probability of observing any value within the distribution is 1 or 100%.
To find the probability associated with a certain area under the normal distribution curve, we can use the cumulative distribution function (CDF). The CDF of a normal distribution gives us the probability that a random variable falls within a specific range.
The total area under the normal distribution curve, also known as the standard normal distribution, is equal to 1 or 100%. This means that the probability of any value falling within the entire range of the normal distribution is 1.
To calculate the probability associated with a specific area under the normal distribution curve, you need to know the z-score, which represents the number of standard deviations a value is from the mean.
The area to the left of a specific z-score can be found using statistical tables or by using software or programming language functions that provide the CDF for the normal distribution. These tables or functions give you the probability of a value being less than or equal to a certain point on the distribution.
For example, if you want to find the probability that a random variable is less than or equal to a certain value x, you can find the corresponding z-score and then look up the probability in the standard normal distribution table or use a function that calculates this for you.
Ultimately, the total area under the normal distribution curve is equal to 1 or 100% because it represents the probability of any value falling within the entire range of the distribution.