Errors in a text are either nonword errors as when typed word errors that result

Question

Errors in a text are either nonword errors as when typed word errors that result in a real but incorrect word Spell checking software will catch nonword errors but not word errors. Human proofreaders catch catch 65% of word errors. You ask a fellow student to proofread an essay in which you have deliberately made 10 word errors. If the student matches the usual 65% rate, what is the distribution of the number of errors caught? What is the distribution of the number of errors missed? Missing three or more out of 10 errors seems a poor performance. What is the probability that a proofreader who catches of word errors misses exactly three out of 10? (Round your answer to four decimal places.) What is the probability of missing three or more out of 10? (Round your answer to four decimal places.)

Explanation / Answer

a) n = 10

p = 0.65

n = 10

p = 1 - 0.65 = 0.35

This is a binomial distribution.

b) P(X = x) = 10Cx * 0.35x * (1 - 0.35)10-x

P(X = 3) = 10C3 * 0.353 * 0.657 = 0.2522

P(X > 3) = 1 - P(X < 3)

               = 1 - [P(X = 0) + P(X = 1) + P(X = 2)]

               = 1 - [10C0 * 0.350 * 0.6510 + 10C1 * 0.351 * 0.659 + 10C2 * 0.352 * 0.658]

               = 1 - 0.2616

               = 0.7384

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