Questions: What is the mean of the standard normal distribution? What is the standard deviation of the standard normal distribution?

What is the mean of the standard normal distribution? What is the standard deviation of the standard normal distribution?
Transcript text: What is the mean of the standard normal distribution? What is the standard deviation of the standard normal distribution? $\qquad$
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Solution

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Solution Steps

Step 1: Calculate the Mean

The mean \( \mu \) of the standard normal distribution is calculated as follows:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} = \frac{0}{1} = 0.0 \]

Thus, the mean of the standard normal distribution is:

\[ \text{Mean of the standard normal distribution: } 0.0 \]

Step 2: Calculate the Variance

The variance \( \sigma^2 \) is calculated using the formula:

\[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{N} = \frac{0.0}{1} = 0.0 \]

Step 3: Calculate the Standard Deviation

The standard deviation \( \sigma \) is the square root of the variance:

\[ \sigma = \sqrt{0.0} = 0.0 \]

Thus, the standard deviation of the standard normal distribution is:

\[ \text{Standard deviation of the standard normal distribution: } 0.0 \]

Final Answer

The mean and standard deviation of the standard normal distribution are:

\[ \boxed{\mu = 0.0 \text{ and } \sigma = 1.0} \]

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