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# Continuous Random Variables

When will that bus finally arrive? How hot is it going to be outside today? These any many other real-world values can be modeled by continuous random variables.

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.

**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 \(\mathbb{E}[(X-\mu_X)^3].\)

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