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How to find the mean and standard deviation of a standard normal distribution?
Statistics is an important branch of mathematics that concerns the collection, organization, analysis, interpretation, and presentation of data. Various parameters like mean, median, and mode are used to analyze data and extract information from them. Here, we will see how to find the mean and standard deviation of standard normally distributed data.
Answer: The mean of a standard normal distribution is zero, and the standard deviation is one.
Let's understand the solution from the given explanation.
For a normal distribution, the mean is the point where its graph attains its peak value, as shown in the figure. In the case of standard normal or Gaussian distribution, this value is attained at x=0. Hence, its mean is zero.
The standard deviation of the standard normal distribution is one.
In general, when a normal distribution is converted to standard normal form, then the random variable is represented by Z = (X - μ) / σ, where μ is the mean and σ is the standard deviation of the normal distribution.
Hence, the mean of a standard normal distribution is zero, and the standard deviation is one.