Question

The average farm in the united states in 2004 contained 443 acres. the standard deviation is 42 acres. suppose the distribution of farm sizes is bell-shaped. according to the empirical rule, what percentage of farms would you expect to be larger than 527 acres. round your answer to one decimal place

Answer 1

2.5%
Let's see how many standard deviations from the norm 527 acres is. (527 - 443)/42 = 84/42 = 2
The empirical rule is that 95% of the data will lie within 2 standard deviations of the norm. But that includes the data that both above and below the mean. So you also say that 2.5% of the data will be greater than 2 standard deviations above the mean and 2.5% less than 2 standard deviations below the mean.
So the answer is 2.5%