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 Discussion Prompt: Probability of Guessing: A friend tells you they only need a 25% on the final exam to pass this statistics class, and since the exams are always multiple choice with four possible answers they can randomly guess at the answers and still get 25%.

(Tip: it may help if you create a table of Binary probabilities with p = 0.25 and n = number of questions on the exam. Also, don’t confuse the probability of getting exactly 25% of the questions correct and getting at least 25% of the questions correct.)

(Minimum word count for initial post = 150 words. Maximum word count = 250)

Discussion Grading Rubric:

I. Student makes a statement about the friend’s choice (10%)
In the second submission/attachment this indicator is highlighted in yellow.

II. Student clearly states why they chose their answer (Up to 20% - see sub-letters)
a. The reasoning is valid and convincing (20%)
b. The reasoning is valid, but vague (15%)
c. The reasoning is valid, but not applicable to the problem (10%)
d. The reasoning is incorrect (0%)
In the second submission/attachment this indicator is underlined.

III. Student has provided a statistical probability for the friend’s chances of getting at least 25% on the exam. (Grading: Up to 30% - see sub-letters)
a. Provides the correct probability, correctly related to the sample size (30%)
b. Provides a reasonable probability, but does not tie the answer to a particular sample size (20%)
c. Provides a non - statistical response (ie: Not very good) (10%)
d. Does not address the friend’s chances. (0%)
In the second submission/attachment this indicator is italicized.

IV. Student addresses the difference sample size makes (Grading: Up to 25% - see sub-letters)
a. Correctly relates the difference to the change in standard deviation vs the change in the range (25%)
b. Correctly identifies the effect of increasing sample size on probability spread around the mean (20%)
c. Correctly relates increased sample size to reduced probability of getting at least 25% on the exam (15%)
d. Incorrectly states increased sample size improves the probability of getting at least 25% on the exam (5%)
e. Does not address the question of sample size (0%)
In the second submission/attachment this indicator is in bold font.

V. Initial post is submitted on time containing very few, if any errors related to grammar, spelling, and sentence structure. Easy to read and understand. Meets the minimum word count. Submitted in the text box, as well as an attached file. Follows all directions in the second submission (Highlighting, italics, underlining, etc.) Two responses are made to classmates. (Minimum word count for initial post = 150 words. Maximum word count = 250.) (15%)
If not responses to others are made, up to two points will be deducted.