## Algebra 2 (1st Edition)

$\text{z-score}=\frac{\text{data item-mean}}{\text{standard deviation}}$ a) $\frac{8-6}{1}=2$ The normal distribution is symmetric about the mean; thus using the 68-95-99.7 rule and the graph we get: $P( x\leq\overline{x}+2\sigma)=50\%+34\%+13.5\%=97.5\%$ b) $\frac{7-6}{1}=1,\frac{4-6}{1}=-2$ The normal distribution is symmetric about the mean; thus using the 68-95-99.7 rule and the graph we get: $P( \overline{x}-2\sigma\leq x\leq\overline{x}+\sigma)=34\%+34\%+13.5\%=81.5\%$