Final answer:
The standard normal distribution is represented by a bell-shaped curve and percentages of data within certain standard deviations are described by the Empirical Rule, which indicates that approximately 68%, 95%, and 99.7% of the data is found within one, two, and three standard deviations of the mean, respectively. The correct answer is B. 95% in the middle, 5% in each tail.
Step-by-step explanation:
The standard normal distribution N(μ = 0, σ = 1) is characterized by its bell-shaped curve that's symmetric about the mean (μ). The distribution can be described by the Empirical Rule, which outlines what percent of the data falls within certain standard deviations of the mean. Here are the percentages for the regions within a standard normal distribution:
In a standard normal distribution with a mean (μ) of 0 and a standard deviation (σ) of 1, approximately 68% of the values fall within one standard deviation of the mean, which is in the middle of the distribution.
However, in a standard normal distribution, approximately 95% of the values fall within two standard deviations of the mean. Therefore, 95% is found in the middle, and the remaining 5% is split equally between the two tails.
It is important to note that this distribution follows the Empirical Rule for a bell-shaped and symmetric distribution.