Answer :
Final answer:
Approximately 16% of the data points are greater than 11 in a normally distributed dataset with a mean of 9.2 and a standard deviation of 1.8, based on the 68 - 95 - 99.7 rule.
Explanation:
According to the 68 - 95 - 99.7 rule (also known as the Empirical Rule), for a normal distribution, approximately 68% of the data points fall within one standard deviation of the mean, about 95% within two standard deviations, and over 99.7% within three standard deviations.
The question states that the mean of the data is 9.2 and the standard deviation is 1.8.
To determine what percentage of data points are greater than 11, we need to calculate how many standard deviations 11 is from the mean.
First, we subtract the mean from 11, which gives us:
11 - 9.2 = 1.8
Since the standard deviation is 1.8, this means that 11 is exactly one standard deviation above the mean. Based on the Empirical Rule, 68% of data falls within one standard deviation of the mean on both sides.
This also implies that 34% of data falls above the mean up to one standard deviation, and another 34% falls below it. Beyond one standard deviation (greater than 11), we have the remaining percentages from the full 100%.
Thus, 100% - 68% = 32% of the data points lie beyond one standard deviation from the mean. However, this 32% is split into two tails of the distribution, so we take half of it to find the percentage greater than 11.
32% / 2 = 16%
Therefore, approximately 16% of the data points are greater than 11.
