Suppose that 10% of the fields in a given agricultural area with about 2,500 fields are infested with the sweet potato white fly. One hundred fields in this area are randomly selected and checked for white fly.

a. Can this be considered an almost binomial situation? Why or why not?

b. Using the exact binomial calculation, what is the probability that from 4 to 16 randomly selected fields are infected?

c. Using the normal approximation, find the probability that between 4 and 16 randomly selected fields are infected. Be sure to check that np ≥ 10 and n(1 – p) ≥ 10. Find the probability in two ways: with and without the continuity correction. How do the answers from the two methods compare, and how do you account for the difference?

d. Sketch the probability distribution and the area you found when using the normal approximation with the continuity correction.