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 20 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

This is binomial distribution with p=0.7 and n=20

Using online calculator we need to find P(x>=m)<=0.05

We get P(x>=18)=0.035483132298469<=0.05

so m=18

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