Question

When scores are normally distributed, where do 95% of these scores fall?

a) Within one standard deviation from the mean
b) Within two standard deviations from the mean
c) Within three standard deviations from the mean
d) Within four standard deviations from the mean

Answer 1

95% of normally distributed scores fall within two standard deviations from the mean, according to the Empirical Rule applied to bell-shaped, symmetric distributions.

Step-by-step explanation:

When scores are normally distributed, 95% of these scores fall within two standard deviations from the mean. This concept is a cornerstone of descriptive statistics and is known as the Empirical Rule. The Empirical Rule states that for a bell-shaped and symmetric distribution, also known as a normal or Gaussian distribution, approximately 68% of the data lies within one standard deviation of the mean, 95% within two standard deviations, and more than 99% within three standard deviations.

This knowledge is crucial when dealing with problems that involve the normal distribution, as it helps to predict how data is spread in relation to the mean. Thus, the correct answer to the question is b) Within two standard deviations from the mean.