In a large class, the distribution of homework scores for homework 1 and homework 2 is approximately
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Question:
In a large class, the distribution of homework scores for homework 1 and homework 2 is approximately bivariate normal. Define the following notation.
- For i = 1, 2, mu_i is the class average on homework i and (sigma_i)^2 is the class variance on homework i.
- The correlation between homework 1 and 2 scores in the class is p.
a) For approximately what proportion of the students was the homework 2 score (in standard units) higher than the homework 1 score (in standard units)?
b) For approximately what proportion of the students did the two homework scores (each in standard units) differ by more than 1?
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