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 10 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.

Respuesta :

The probability that a proofreader who catches 70% of the word errors misses exactly 7 out of 10 will be 0.3504.

How to calculate the probability?

It should be noted that this is a binomial distribution.

From the information given, the human proofreaders catch 70% of word errors and a student was asked to proofread an essay in which you have deliberately made 10 word errors.

Here, n = 10

p = 0.3,

q = 1 - 0.3 = 0.7.

The probability will be:

= 1 - (10C0 × 0.3ⁿ × 0.7^10 + 10C1 × 0.3 × 0.7^9 + 10C2 × 0.3² × 0.7^8 + 10C3 × 0.3³ × 0.7^7)

= 1 - 0.6496

= 0.3504

In conclusion, the probability is 0.3504.

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