Students in a large botany class conducted an experiment on the germination of seeds of the Saguaro cactus. As part of the experiment, each student planted five seeds in a small cup, kept the cup near a window, and checked every day for germination (sprouting). The class results on the seventh day after planting were as displayed in the table.

(a) Fit a binomial distribution to the data. (Round the expected frequencies to one decimal place.)
(b) Two students, Fran and Bob, were talking before class. All of Fran's seeds had germinated by the seventh day, whereas none of Bob's had. Bob wondered whether he had done something wrong. With the perspective gained from seeing all 280 students' results, what would you say to Bob?
(c) Invent a fictitious set of data for 280 students, with the same overall percentage germination as the observed data given in the table, but with all the students getting either Fran's results (perfect) or Bob's results (nothing). How would your answer to Bob differ if the actual data had looked like this fictitious data set?

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Number of seeds Number of Germinated Not germinated students 17 53 94 79 4 4 Total 280