143 Efficacy of an insecticide. The efficacy of insecticides is often measured by the dose necessary to kill a certain percentage of insects. Suppose a certain dose of a new insecticide is supposed to kill 80% of the insects that receive it. To test the claim, 25 insects are exposed to the insecticide.

a. If the insecticide really kills 80% of the exposed insects, what is the probability that fewer than 15 die?

b. If you observed such a result, what would you conclude about the new insecticide? Explain your logic.