Typographic errors. In the proofreading setting of given Exercise, what is the smallest number of misses m with P(X ≥ m) no larger than 0.05? You might consider m or more misses as evidence that a proofreader actually catches fewer than 70% of word errors.
Exercise
Typographic errors. Typographic errors in a text are either nonword errors (as when "the" is typed as "teh") or word errors that result in a real but incorrect word. Spell-checking software will catch nonword errors but not word errors. Proofreaders who are not professionals catch 70% of word errors. You ask a fellow student to proofread an essay in which you have deliberately made 10 word errors.
(a) If the student matches the usual 70% rate, what is the distribution of the number of errors caught? What is the distribution of the number of errors missed?
(b) Missing 4 or more out of 10 errors seems a poor performance. What is the probability that a proofreader who catches 70% of word errors misses 4 or more out of 10?