Continuous Random Variables: Key Takeaways

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For a continuous random variable $X$ the only probabilities that are computed are those of $X$ taking a value in a specified interval.
The probability that $X$ take a value in a particular interval is the same whether or not the endpoints of the interval are included.
The probability $P(a < X < b)$ , that $X$ take a value in the interval from $a$ to $b$ , is the area of the region between the vertical lines through $a$ and $b$ , above the $x$ -axis, and below the graph of a function $f(x)$ called the density function.
A normally distributed random variable is one whose density function is a bell curve.
Every bell curve is symmetric about its mean and lies everywhere above the $x$ -axis, which it approaches asymptotically (arbitrarily closely without touching).