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Essay errors Typographical and spelling errors can be either nonword errors or word
Chapter 6, Problem 51(choose chapter or problem)
Typographical and spelling errors can be either “nonword errors” or “word errors.” A nonword error is not a real word, as when “the” is typed as “teh.” A word error is a real word, but not the right word, as when “lose” is typed as “loose.” When students are asked to write a 250-word essay (without spell-checking), the number of nonword errors X in a randomly selected essay has the following probability distribution:
\(\begin{array}{lccccc} \hline \text { Value: } & 0 & 1 & 2 & 3 & 4 \\ \text { Probability: } & 0.1 & 0.2 & 0.3 & 0.3 & 0.1 \\ \hline \end{array}\)
\(\mu_X=2.1\quad\ \ \ \ \ \sigma_X=1.136\)
The number of word errors Y has this probability distribution:
\(\begin{array}{lcccc} \hline \text { Value: } & 0 & 1 & 2 & 3 \\ \text { Probability: } & 0.4 & 0.3 & 0.2 & 0.1 \\ \hline \end{array}\)
\(\mu_Y=1.0\quad\ \ \ \ \ \sigma_Y=1.0\)
Assume that X and Y are independent.
An English professor deducts 3 points from a student’s essay score for each nonword error and 2 points for each word error. Find the mean and standard deviation of the total score deductions for a randomly selected essay. Show your work.
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QUESTION:
Typographical and spelling errors can be either “nonword errors” or “word errors.” A nonword error is not a real word, as when “the” is typed as “teh.” A word error is a real word, but not the right word, as when “lose” is typed as “loose.” When students are asked to write a 250-word essay (without spell-checking), the number of nonword errors X in a randomly selected essay has the following probability distribution:
\(\begin{array}{lccccc} \hline \text { Value: } & 0 & 1 & 2 & 3 & 4 \\ \text { Probability: } & 0.1 & 0.2 & 0.3 & 0.3 & 0.1 \\ \hline \end{array}\)
\(\mu_X=2.1\quad\ \ \ \ \ \sigma_X=1.136\)
The number of word errors Y has this probability distribution:
\(\begin{array}{lcccc} \hline \text { Value: } & 0 & 1 & 2 & 3 \\ \text { Probability: } & 0.4 & 0.3 & 0.2 & 0.1 \\ \hline \end{array}\)
\(\mu_Y=1.0\quad\ \ \ \ \ \sigma_Y=1.0\)
Assume that X and Y are independent.
An English professor deducts 3 points from a student’s essay score for each nonword error and 2 points for each word error. Find the mean and standard deviation of the total score deductions for a randomly selected essay. Show your work.
ANSWER:Step 1 of 3
Given,
X = the number of nonword errors in a randomly selected essay.
The mean no. of nonword errors, \(\mu_{X}=2.1\)
The standard deviation of no. of nonword errors, \(\sigma_{X}=1.136\)
Y = The number of word errors in a randomly selected essay.
The mean no. of word errors, \(\mu_{Y}=1.0\)
The standard deviation of no. of word errors, \(\sigma_{Y}=1.0\)
Let’s find the mean and standard deviation of the total score deductions for a randomly selected essay:
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