IT 223: Data Analysis
Winter 2006
Assignment 6
Proportions and Counts
A proofreader claims to catch 80% of a word errors. You hire the
proofreader to check a report that you wrote where you deliberately
create 50 word mistakes in an otherwise perfect report.
For the following questions, assume that the proofreader's claim is
true.
Helpful hint: think of each word error as having one of two
possible outcomes: caught or not caught. What kind of setting is
this?
- Describe the distribution of the number of word errors that would
be caught by the proofreader. The distribution should be described in
terms of mean and standard deviation.
- What is the probability that at least 45 of the 50 word errors
will be caught?
- Describe the distribution of the proportion of
word errors that would be caught by the proofreader. The distribution
should be described in terms of mean and standard deviation.
- What is the probability that the proofreader will catch at least
.7 (or 70%) of the word errors?
Dice Rolling Revisited
Returning to the repeated rolls of 50 dice from last week...
- What is the expected mean of rolling 50 6-sided dice? (hint: it's the same as the expected mean of one die)
- What is the standard error, that is, what is the standard deviation of means from samples?
- What percentage of the rolls would you expect be within one
standard error of the expected mean?
- Use this new applet to simulate
1000 samples of 50 dice. These results can be easily pasted into Excel
and sorted (under the Data menu). What percentage of the 1000 rolls
were actually within one standard error of the expected mean?
Submission
Submit a one-document report that responds to the
instructions. Show your work.