Which of the following is a characteristic of the standard normal distribution?
A
It is skewed to the right.
B
It has a mean of and a standard deviation of .
C
Its total area under the curve is less than .
D
It has a mean of and a standard deviation of .
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1
Recall that the standard normal distribution is a special case of the normal distribution with specific parameters.
Identify the mean (\( \mu \)) and standard deviation (\( \sigma \)) of the standard normal distribution. By definition, \( \mu = 0 \) and \( \sigma = 1 \).
Understand that the standard normal distribution is symmetric about the mean, so it is not skewed to the right or left; it has zero skewness.
Remember that the total area under the probability density curve of any normal distribution, including the standard normal, is exactly 1, representing the total probability.
Evaluate each option based on these properties: the correct characteristic is that the standard normal distribution has a mean of 0 and a standard deviation of 1.