5.55 Number of aphids. The milkweed aphid is a common pest to many ornamental plants. Suppose that the number of aphids on a shoot of a Mexican butterfly weed follows a Poisson distribution with ? = 4.4 aphids. (a) What is the probability of observing exactly five aphids on a shoot? (b) What is the probability of observing five or fewer aphids on a shoot? 5.56 Number of aphids, continued. Refer to the previous exercise. (a) What proportion of shoots would you expect to have no aphids present? (b) If you do not observe any aphids on a shoot, is the probability that a nearby shoot has no aphids smaller than, equal to, or larger than your answer in part (a)? Explain your reasoning.
Added by Jeffrey E.
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Using the Poisson distribution formula, we have: \[ P(X = 5) = \frac{e^{-4.4} \times 4.4^5}{5!} \] \[ P(X = 5) = 0.1687 \] Show more…
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