(14.09) Typing errors in a text are either nonword errors (as when the is typed

Question

(14.09) 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.

Step 1:
If X is the number of word errors missed, what is the distribution of X?

Step 2:
If Y is the number of word errors caught, what is the distribution of Y?

Step 3:
What is the mean number of errors caught?
Give your answer as a whole number.

Step 4:
What is the mean number of errors missed?
Give your answer as a whole number.

Step 5:
What is the standard deviation of the number of errors caught?
Give your answer to 4 decimal places.

Step 6:
What is the standard deviation of the number of errors missed?
Give your answer to 4 decimal places.

(14.09) 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.

Step 1:
If X is the number of word errors missed, what is the distribution of X?

A. X is binomial with n = 10 and p = 0.3. B. X is approximately Normal with = 3 and = 1.45. C.X is Normal with = 7 and = 1.45. D. X is binomial with n = 10 and p = 0.7.

Step 2:
If Y is the number of word errors caught, what is the distribution of Y?

A. Y is approximately Normal with = 3 and = 1.45. B. Y is binomial with n = 10 and p = 0.7. C. Y is binomial with n = 10 and p = 0.3. D. Y is Normal with = 7 and = 1.45.

Step 3:
What is the mean number of errors caught?
Give your answer as a whole number.

Step 4:
What is the mean number of errors missed?
Give your answer as a whole number.

Step 5:
What is the standard deviation of the number of errors caught?
Give your answer to 4 decimal places.

Step 6:
What is the standard deviation of the number of errors missed?
Give your answer to 4 decimal places.

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Explanation / Answer

Step 1:
If X is the number of word errors missed, then the distribution of x is

Step 2:
If Y is the number of word errors caught, then the distribution of Y is

Y is binomial with n = 10 and p = 0.7.

Step 3:
What is the mean number of errors caught?
mean= np =10*0.7=7

Step 4:
What is the mean number of errors missed?
mean= np =10*0.3=3

Step 5:

What is the standard deviation of the number of errors caught?
standard dev= sqrt(npq) =sqrt(10*0.7*.3) = 1.4491

Step 6:
What is the standard deviation of the number of errors missed?
standard dev= sqrt(npq) =sqrt(10*0.3*.0.7) = 1.4491

X is binomial with n = 10 and p = 0.3.

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