The mean of a normally distributed data set is 12, and the standard deviation is 2.
___% of the data points lies between 8 and 16.
Find the percentage
8 is 2 std below the mean
16 is 4 std above the mean
P(Z>4) = .9772
P(Z>8) = .0227
P(4<Z<8) = .9772-.0228 = .9545
You can play around with this stuff at
http://davidmlane.com/hyperstat/z_table.html
To find the percentage of data points that lie between 8 and 16 in a normally distributed data set with a mean of 12 and a standard deviation of 2, you can use the empirical rule, also known as the 68-95-99.7 rule.
According to this rule, for a normally distributed data set:
- Approximately 68% of the data points fall within one standard deviation of the mean.
- Approximately 95% of the data points fall within two standard deviations of the mean.
- Approximately 99.7% of the data points fall within three standard deviations of the mean.
In this case, the interval 8 to 16 is within 2 standard deviations of the mean (12 - 2 = 10 and 12 + 2 = 14). So, approximately 95% of the data points will fall between 8 and 16.
Therefore, the answer is that approximately 95% of the data points lie between 8 and 16.
To find the percentage of data points that lie between 8 and 16 in a normally distributed data set, we can use the empirical rule (also known as the 68-95-99.7 rule).
According to the empirical rule:
- Approximately 68% of the data points lie within one standard deviation (2) of the mean (12).
- Approximately 95% of the data points lie within two standard deviations (2 * 2 = 4) of the mean.
- Approximately 99.7% of the data points lie within three standard deviations (3 * 2 = 6) of the mean.
Since the distance between the mean (12) and 8 is 4 and the distance between the mean (12) and 16 is also 4, we can use the empirical rule to estimate the percentage of data points that fall between 8 and 16.
Since this range falls within two standard deviations from the mean, we know that approximately 95% (as per the empirical rule) of the data points lie between 8 and 16 in a normally distributed data set.
Therefore, approximately ___% of the data points lie between 8 and 16.