Question

Given the question:

"Researchers found that 25% of the beech trees in east central Europe had been damaged by fungi. Consider a sample of 20 beech trees from this area.

How many of the sampled trees would you expect to be damaged by fungi?"

I was asked, "The question as asked is misleading, why? Nevertheless, give a numerical answer."

I don't see how this question is misleading. All I can think of it asking for is expected value, which would be µ = (0.25)(20) = 5. So my question is not what the expected value is, my question is how is the question misleading, what am I missing here?

Answer 1

The number of beech trees that are damaged by fungi could be modelled here as a binomial distribution given as:

The expected number of trees that are damaged by fungi could be computed here as:

E(X) = np = 20*0.25 = 5

Therefore 5 is the expected or the mean number of trees that would be damaged by fungi out of the 20 trees.

The question can be misleading in the sense that we are are assuming here as a property of the binomial distribution that the events are independent, which means that given that there is a fungi infected tree, it wont have an effect on the other tree which is not actually correct here. It is very intuitive that the fungi infection spreads from trees to trees. Therefore given a fungi infected tree, it increases the probability of other tree having a fungi infection. Therefore the assumption of independence might not hold in this case and therefore the question could be misleading.