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

The probability that he will miss the error is 1 - 0.70 = 0.3.

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    15      
p = the probability of a success =    0.3      
x = our critical value of successes

Then the cumulative probability of P(at most x - 1) from a table/technology must satisfy          
          
P(at most   m - 1   ) > 0.95
          
Using a table, we see that the least m that will satisfy his is m-1 = 8, or

m = 9 [ANSWER]

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[Actually, m = 8 is quite close, but not reallt less than 0.05. It is 0.05001254, so we cannot accept it.]

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