Question: Typographic errors in a test are either non-word errors (as when the is typed as teh) or word errors that result in a real but

Typographic errors in a test are either non-word errors (as when "the" is typed as "teh") or word errors that result in a real but incorrect word. Spell-checking software will catch non-word 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 20word errors.

(a) If the number of errors caught matches the usual 70% rate, what is the distribution of the number of errors missed?

(b) Missing 9 or more out of 20 errors seems a poor performance. What is the probability that a proofreader who catches 70% of word errors on average misses 9 or more out of 20?

(c) What is the mean number of errors caught? What is the mean number of errors missed? You see that these two means must add to 20, the total number of errors.

(D) What is the standard deviation of the number of errors caught?

(e) Suppose that a professor catches 90% of word errors, so that p=0.9. What is standard deviation in this case? What is standard deviation if p=0.99? What happens to the standard deviation of a binomial distribution as the probability of a success gets close to 1?

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