At the Dr T $\frac { 1 } { \sqrt { 2 \pi } } e ^ { - x ^ { 2 } / 2 }$

At the Dr. T. Bottling Company, the amount of soda dispensed into the cans is normally distributed so the probability that a can will contain a certain amount of soda may be calculated using the area under the curve y = p (x), where p(x) = $\frac { 1 } { \sqrt { 2 \pi } } e ^ { - x ^ { 2 } / 2 }$ Use your graphing calculator to produce a graph of this function.(a) The probability that a can will contain between 12.0 and 12.2 ounces of soda is given by $\int _ { - 0.22 } ^ { 0.22 } \frac { 1 } { \sqrt { 2 \pi } } e ^ { - x ^ { 2 } / 2 } d x$ Use Simpson's Rule with n = 4 to approximate this probability.(b) The probability that a can will contain at least 12 ounces of soda is given by $\int _ { - 0.22 } ^ { \infty } \frac { 1 } { \sqrt { 2 \pi } } e ^ { - x ^ { 2 } / 2 } d x$ What is the approximate value of this integral?