Typographic errors in a text are either nonword errors (as when \"the\" is typed
ID: 3205953 • Letter: T
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 12 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.
Explanation / Answer
Result:
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 12 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.
P(Success) = .7; P(Failure) = 1 - P(Success) = .3
we have a total of 12 trials. n=12
p= probability of misses= 0.3
P(X=x) = (nCx) px (1-p)n-x
Binomial Probabilities Table
X
P(X)
0
0.0138
1
0.0712
2
0.1678
3
0.2397
4
0.2311
5
0.1585
6
0.0792
7
0.0291
8
0.0078
9
0.0015
10
0.0002
11
0.0000
12
0.0000
From table P(X 7) no larger than 0.05.
The required number of misses = 7
Binomial Probabilities Table
X
P(X)
0
0.0138
1
0.0712
2
0.1678
3
0.2397
4
0.2311
5
0.1585
6
0.0792
7
0.0291
8
0.0078
9
0.0015
10
0.0002
11
0.0000
12
0.0000
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