For a standard normal distribution, what is the approximate probability that a randomly selected value lies between -1 and 1?
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Correct answer
B. 68%
Principle or equation
The empirical rule (68-95-99.7 rule) states that in a normal distribution, about 68% of data falls within one standard deviation of the mean.
Why this answer is correct
In a standard normal distribution, the mean is 0 and standard deviation is 1. The interval (-1, 1) is within one standard deviation of the mean. By the empirical rule, approximately 68% of the data lies in this interval.
Example
If IQ scores are normally distributed with mean 100 and SD 15, about 68% of people have IQ between 85 and 115.
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