Question

Typing 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. (a) If ? is the number of word errors missed, what is the distribution of ? ? Select an answer choice. ? is binomial with ?=10 and ?=0.7 ? is Normal with ?=7 and ?=1.45 ? is binomial with ?=10 and ?=0.3 ? is approximately Normal with ?=3 and ?=1.45 If ? is the number of word errors caught, what is the distribution of ? ? Select an answer choice. ? is binomial with ?=10 and ?=0.3 ? is binomial with ?=10 and ?=0.7 ? is approximately Normal with ?=3 and ?=1.45 ? is Normal with ?=7 and ?=1.45 (b) What is the mean number of errors caught? (Enter your answer as a whole number.) mean of errors caught = What is the mean number of errors missed? (Enter your answer as a whole number.) mean of errors missed = (c) What is the standard deviation of the number of errors caught? (Enter your answer rounded to four decimal places.) standard deviation of the number of errors caught = What is the standard deviation of the number of errors missed? (Enter your answer rounded to four decimal places.) standard deviation of the number of errors missed =

Answer 1

Probability that an error is caught = 0.7

So probability that an error is missed = 0.3

a) So, X~Binomial n=10, p= 0.3

And Y~Binomial n=10, p=0.7

b) Mean number of errors caught = n*p= 10*0.7=7

So, mean number of errors missed = 10*0.3 = 3

c) Standard deviation of the number of errors caught = √np(1-p) = 1.4491

Standard deviation of the number of errors missed = 1.4491