145k views
2 votes
In the normal distribution, what percentage of scores fall within one standard deviation of the mean?

a. 33%
b. 50%
c. 68%
d. 75%
e. 90%

User LonelySoul
by
8.3k points

1 Answer

6 votes

Final answer:

Approximately 68% of scores in a normal distribution fall within one standard deviation of the mean, as part of the Empirical Rule for bell-shaped, symmetric distributions.

Step-by-step explanation:

In the normal distribution, approximately 68% of scores fall within one standard deviation of the mean. This is a key aspect of the Empirical Rule, which applies to data that has a bell-shaped, symmetric distribution. To further elaborate, approximately 95% of scores lie within two standard deviations of the mean, and more than 99% fall within three standard deviations of the mean.

For example, if the mean (average) of a normal distribution is 50 and the standard deviation is 6, then 68% of the x values would lie between 44 (50 - 6) and 56 (50 + 6). These intervals correspond to z-scores of -1 and +1, respectively, for the values at 44 (one standard deviation below the mean) and 56 (one standard deviation above the mean).

User Ramanman
by
7.7k points