Final answer:
In a normal distribution, values are distributed around a mean and the spread is measured by the standard deviation, indicating the variation of the data. A bell-shaped distribution with a mean of 0 and standard deviation of 1 is referred to as a standard normal distribution. The empirical rule states that about 95% of data falls within two standard deviations of the mean in a normal distribution.
Step-by-step explanation:
In a normal distribution, the values of a variable are distributed around a mean within a certain spread, which indicates the amount of variation in the variable. This spread is most commonly measured by the standard deviation, a number that measures how far data values are from their mean. The normal distribution is a bell-shaped continuous random variable with the center at the mean value (μ) and the spread determined by the standard deviation (σ).
For a standard normal distribution, the mean is 0 and the standard deviation is 1. The variability of the data can be small with values concentrated close to the mean, or it can be large if the data values show more variation. Significant spread in the data, represented by a high standard deviation, can suggest the presence of outliers or a wider range of values.
The empirical rule helps to understand the spread within a normal distribution, stating that approximately 95% of the data is within two standard deviations of the mean. This rule is particularly useful in determining the spread and the normal range for datasets that have a bell-shaped distribution pattern.