It has a mean of zero and a standard deviation of one. The standard normal distribution is a special case of the normal distribution. It is a versatile distribution that is often used to model normally distributed data, such as height or intelligence. These are some of the most important properties of normal distribution.
This is often referred to as the 68-95-99.7 rule. 68-95-99.7 rule: The normal distribution has the property that, for a given standard deviation, approximately 68% of the values will fall within one standard deviation of the mean, 95% of the values will fall within two standard deviations of the mean, and 99.7% of the values will fall within three standard deviations of the mean.This means that the probability of a value being close to the mean is higher than the probability of a value being far from the mean. Bell-shaped curve: The normal distribution has a bell-shaped curve.This means that the probability of a value being extremely large or extremely small is always non-zero but becomes increasingly small as the value becomes more extreme. Asymptotic behaviour: The normal distribution approaches but never reaches the x-axis as the values of x become increasingly large.This peak is located at the mean of the distribution. Unimodality: The normal distribution is unimodal, meaning that it has a single peak.This means that the probability of a value being above the mean is equal to that of a value being below the mean. Symmetry: The normal distribution is symmetrical around the mean.It has several important properties, including: The normal distribution is a continuous probability distribution that is defined by two parameters: the mean and the standard deviation. The normal distribution is one of the most commonly used distributions in statistics. It is also known as the Gaussian distribution, after the mathematician Carl Friedrich Gauss who first described it. The normal distribution is a probability distribution that is used to describe many natural phenomena.
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