please solve the problems "by hand" you may do partial calculations in R though

show detailed works and steps, if use R show the commands.

please don't just give me an R output Please provide detailed steps how you get the answers.

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A paper in the the Annals of Mathematical Statistics reports the fol- lowing data on the number of borers in each of 120 group borers. Does the Poisson distribution provide a plausible model for the distribution of the number of borers in a group? Number of borers 0 1 2 3 4 5 6 7 8 9 10 11 12 Frequency 24 16 16 18 15 9 6 5 3 4 3 0)