Researchers in the Hopkins Forest (see Exercise 7-16) also count the number of maple trees (genus acer) in plots throughout the forest. The following is a histogram of the number of live maples in 1002 plots sampled over the past 20 years. The average number of maples per plot was 19.86 trees with a standard deviation of 23.65 trees. 

(a) If we took the mean of a sample of eight plots, what would be the standard error of the mean?

(b) Using the central limit theorem, what is the probability that the mean of the eight would be within 1 standard error of the mean?

(c) Why might you think that the probability that you calculated in (b) might not be very accurate?

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500 300 100 150 50 100 200 250 Number of trees Number of plots