Multiple Choice
For the standard normal probability distribution, what are the mean and standard deviation ?
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6. Normal Distribution and Continuous Random Variables
Standard Normal Distribution
Multiple Choice
Which of the following statements is true about the standard normal distribution?
A
Its total area under the curve is less than .
B
It has a mean of and a standard deviation of .
C
It is skewed to the right.
D
It has a mean of and a standard deviation of .
Verified step by step guidance1
Recall the definition of the standard normal distribution: it is a normal distribution with a mean (\(\mu\)) of 0 and a standard deviation (\(\sigma\)) of 1.
Understand that the total area under any probability density function (PDF) curve, including the standard normal distribution, must equal 1 because it represents the total probability.
Recognize that the standard normal distribution is symmetric about its mean, so it is not skewed to the right or left; it has zero skewness.
Note that a standard deviation of 0 is not possible for a normal distribution because it would imply no variability, which contradicts the properties of a normal distribution.
Based on these points, identify the true statement as the one that says the standard normal distribution has a mean of 0 and a standard deviation of 1.
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