Standard normal distribution has which of the following properties

General
1

standard normal distribution has which of the following properties

2

LectureNotes said standard normal distribution has which of the following properties

Answer: Standard normal distribution, also known as the Z-distribution, has several key properties:

  1. Mean and Standard Deviation: The mean of the standard normal distribution is 0, while the standard deviation is 1. This allows for a standardized comparison of data points.

  2. Symmetry: The standard normal distribution is symmetric around the mean, which is located at 0. The distribution curve is bell-shaped.

  3. Area Under the Curve: The total area under the curve of the standard normal distribution is equal to 1, representing the probability of all possible outcomes.

  4. Z-Scores: Standard normal distribution uses Z-scores to calculate the distance of a data point from the mean in terms of standard deviations. This allows for comparison and statistical analysis.

  5. 68-95-99.7 Rule: This rule states that for normal distribution, about 68% of the data falls within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.

  6. Transformation: Any normal distribution with a different mean and standard deviation can be transformed into a standard normal distribution through a process called standardization.

Understanding these properties of standard normal distribution is crucial in various fields like statistics, probability theory, and hypothesis testing.