Continuous Random Variables
True or false: If two distributions have the same mean and standard deviation, they must be the same.
Scores on a certain test have a mean of 75 and standard deviation of 5. Out of 100 random test papers, how many (rounded to the nearest integer) do we expect to have a score of at least 85?
Note: We cannot assume the distribution of scores is normal or approximately normal, we only know its mean and standard deviation.
At a certain company, the distribution of salaries is unimodal and skewed right. The company wants to entice outside workers to join, and thus wants to provide a measure of what a typical employee earns that is as high as possible. Which should they use?
Note: The kurtosis of some random variable \(X\) with standard deviation 1 is \(\mathbb{E}[(X-\mu_X)^4].\)
Note: The skew of a random variable \(X\) has the same sign as \(\mathbb{E}[(X-\mu_X)^3].\)