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 15 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.

? misses

Explanation / Answer

mean = np = 15 * 0.3 = 4.5

standard error = sqrt( 15 * 0.7 * 0.3) = 1.7748

P(X >= m ) <= 0.05

=>

P(Z > m- 4.5/1.7748/sqrt(15)) <= 0.05

m -4.5/1.7748/sqrt(15) <= 1 - invnorm(0.05)

=>

m -4.5 / 1.7748/sqrt(15) = 1 - (-1.645)

m = 5.71

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