Multiple Choice
If an observation has a z-score of in the standard normal distribution, what does this indicate about the observation's value relative to the mean?
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6. Normal Distribution and Continuous Random Variables
Standard Normal Distribution
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Which of the following is a characteristic of the standard normal probability distribution?
A
Its mean and median are not equal.
B
It is skewed to the right.
C
It has a mean of and a standard deviation of .
D
It has a variance of .
Verified step by step guidance1
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, the mean is 0 and the standard deviation is 1.
Understand that the standard normal distribution is symmetric about its mean, so the mean, median, and mode are all equal.
Recognize that the standard normal distribution is not skewed; it has a skewness of 0, meaning it is perfectly symmetric.
Note that the variance (which is the square of the standard deviation) of the standard normal distribution is 1, not 0.5.
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