Typographic errors in a text are either nonword errors (as when \"the\" is typed

Question

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. Human proofreaders catch 70% of word errors. You ask a fellow student to proofread an essay in which you have deliberately made 12 word errors. 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.

Explanation / Answer

Solution:-

p = 70/100

p = 0.70

P(misses) = 0.30

We have

P(X > m) = 0.05

n = 12

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x > 7) = 0.0386

Hence the smallest number of misses m with P(X m) no larger than 0.05 is 7 misses.

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