What percentage of the data, distributed normally and with the standard deviation, will fall within 2 standard deviations of the mean?
A)
13.5%
B)
34%
C)
68%
D)
95%
E)
99%
95
You can play around with Z table stuff here:
http://davidmlane.com/hyperstat/z_table.html
The correct answer is C) 68%.
In a normal distribution, approximately 68% of the data falls within 1 standard deviation of the mean. If we double the standard deviation (2 standard deviations), the percentage of the data within that range remains the same.
To find the percentage of data that falls within a certain range of standard deviations from the mean in a normal distribution, you can use the empirical rule, also known as the 68-95-99.7 rule. This rule states that:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
Since the question asks for the percentage of data that falls within 2 standard deviations of the mean, the correct answer is D) 95%.