3. Typographic errors in a text are either non-word errors( as when the is typed

Question

3. Typographic errors in a text 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 10 word errors. a). If the student matches the usual 70% rate, what is the distribution of the number of errors caught? What is the distribution of number of errors missed? b). Missing 4 or more out of 10 errors seems a poor performance. What is the probability that a proofreader who catches 70% of word errors misses 4 or more out of 10? 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 10, the total number of errors. d). What is the standard deviation of the number of errors caught?

Explanation / Answer

Ans:

a)Number of errors caught will have binomial distribution with n=10,p=0.7

Number of errors missed will have binomial distribution with n=10,p=0.3

b)P(x=k)=10Ck*0.3k*(1-0.3)10-k

Probability of missing 4 or more errors=P(x>=4)

=1-P(x<=3)

=1-0.0282-0.1211-0.2335-0.2668

=0.3504

c)mean number of errors caught=np=10*0.7=7

mean number of errors missed=n(1-p)=10*0.3=3

d)standard deviation of errors caught=sqrt(10*0.3*0.7)=1.45

x p(x) 0 0.0282 1 0.1211 2 0.2335 3 0.2668 4 0.2001 5 0.1029 6 0.0368 7 0.0090 8 0.0014 9 0.0001 10 0.0000

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