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. ________ misses (an exact number)

Explanation / Answer

Here we have to find the word errors misses .

we are given ,p=proportion of word error =0.70

And margin of error ( E) =0.05

confidence level is 70%

Zc for 70% is 0.80

n=number of word error misses

formula of n=p*(1-p)*(Zc/E)^2

=0.70*0.30*(0.80/0.050^2

=54.07

n=54

smallest number of misses =54

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