a) For the first question, we're looking at the cumulative probability from a binomial distribution: For example you can use 1-binom.dist(x-1,trials,p,1) in Excel, where x is the minimum number of male wolves (6) and p is the probability of each wolf being male (0.6). Since the total probability of 6+ male wolves out of 9 is 1 minus the probability of 5 male wolves or fewer, we can get this by 1-binom.dist(5,9,0.6,1) = 0.483.
For the second, similarly, we have 1-binom.dist(5,9,0.4,1) = 0.099 (the only difference is that p =0.4 for this question).
To find fewer than three, you can find the cumulative probability up to 2, i.e. binom.dist(2,9,0.4,1) = 0.232. Note we don't need the 1- at the beginning since we're now measuring the area of the distribution from 0 to 2 (fewer than 3 wolves).
b) These are identical questions, but with the probabilities slightly changed. Now we get 0.609, 0.054 and 0.337 respectively. This makes sense - the probability of lots of males increases, while the probability of lots of females decreases, because the individual probabilities for each have shifted towards males.
Feb 27th, 2015
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