**Properties of a Normal Distribution**
$\cdot$ About 68% of the population are within 1 standard deviation of the mean.

$\cdot$ About 95% of the population are within 2 standard deviations of the mean.

$\cdot$ About 99.7% of the population are within 3 standard deviations of the mean.

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**Calculator Commands**
$\cdot$ To calculate the normal distribution probability between two data values:

**normalcdf (lower bound, upper bound, mean, standard deviation)**
- To calculate the area to the

**left **of a data value, replace the

**lower bound** by

$-1 \times 10^{99}$
- To calculate the area to the

**right **of a data value, replace the

**upper bound** by

$1 \times 10^{99}$
$\cdot$ To calculate a data value, given the area to the left of the data value:

** invNorm (area, mean, standard deviation)**