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 10 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

Here given that probability of catch error =0.7; and number of mistakes made n =10

let x be number of errors that missed by a proof reader, so x follows binomial distribution. since the events are random and probability of catching/missing an error is same .

we need to find the smallest number in such a way that

P(x>=m) <= 0.05

P(x>=m) = sum (m to 10 ) (10 C m) (0.3)^m * (0.7) 10-m <= 0.05

From trial and error, P(x>=6)=0.0473 which is less than 0.05

hence the minimum number of misses = 6

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