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### Normal Calculations

There are two classes of problems that we typically solve using a normal distribution:

• For X values a and b, we want to solve for Pr(a ≤ X ≤ b). In these problems, we are solving for cumulative probability.

• For a probability value, p, we want to solve to find x* such that Pr(X≤ x*) = p. In these problems, we are solving for inverse cumulative probability.

For the sake of illustration, let's consider a normal distribution that shares the same mean and standard deviation as the sample of systolic blood pressure measurements. Figure 6.4 displays the summary statistics for our sample of 6, 668 readings. The sample mean is 119.044 mgHg and the sample standard deviation is 18.841 mmHg. For the sake of this illustration, then, we'll ...

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