Answer:
Approximately 2.5% of the data is greater than 34.
Explanation:
To solve this problem, we need to use the empirical rule (also known as the 68-95-99.7 rule) for a normal distribution. This rule states that about 68% of values lie within 1 standard deviation of the mean, about 95% of the values lie within 2 standard deviations of the mean, and about 99.7% of the values lie within 3 standard deviations of the mean.
The mean of the dataset is 27, and the standard deviation is 3.5.
34 is exactly 2 standard deviations away from the mean (since 27 + 2*3.5 = 34). According to the empirical rule, about 95% of the data falls within this range. This means that about 5% of the data is outside of this range.
Since the normal distribution is symmetrical, the data outside of 2 standard deviations is equally split between values that are too large and too small. Hence, about half of this 5%, or 2.5%, is greater than 34.
Therefore, approximately 2.5% of the data is greater than 34.