����app

The standard normal distribution is a special case of the normal distribution where the mean is 0 and the standard deviation is 1. It is represented by the bell-shaped curve, which is symmetric about the mean. This distribution is crucial for statistical analysis as it allows for the calculation of probabilities and z-scores, which indicate how many standard deviations an element is from the mean.

A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It is calculated by subtracting the mean from the value and then dividing by the standard deviation. Z-scores are essential for understanding how far away a particular score is from the average, allowing for comparisons across different datasets.

In the context of the normal distribution, the area under the curve represents the probability of a random variable falling within a particular range. The total area under the curve equals 1, and specific areas correspond to probabilities associated with z-scores. For example, the shaded area in the provided graph indicates the probability of obtaining a z-score less than 0, which is 0.3050.