Questions: Determine the total area under the standard normal curve for parts (a) through (c) below. For each, be sure to draw a standard normal curve and shade the area that is to be found. (a) Determine the total area under the standard normal curve to the left of z=-1 or to the right of z=1. The total area under the standard normal curve to the left of z=-1 or to the right of z=1 is 0.3174 . (b) Determine the total area under the standard normal curve to the left of z=-1.59 or to the right of z=2.59.

Determine the total area under the standard normal curve for parts (a) through (c) below. For each, be sure to draw a standard normal curve and shade the area that is to be found.
(a) Determine the total area under the standard normal curve to the left of z=-1 or to the right of z=1.
The total area under the standard normal curve to the left of z=-1 or to the right of z=1 is 0.3174 .
(b) Determine the total area under the standard normal curve to the left of z=-1.59 or to the right of z=2.59.

Transcript text: Determine the total area under the standard normal curve for parts (a) through (c) below. For each, be sure to draw a standard normal curve and shade the area that is to be found. (a) Determine the total area under the standard normal curve to the left of $z=-1$ or to the right of $z=1$. The total area under the standard normal curve to the left of $z=-1$ or to the right of $z=1$ is 0.3174 . (b) Determine the total area under the standard normal curve to the left of $z=-1.59$ or to the right of $z=2.59$.

Solution

Solution Steps

Step 1: Determine the total area under the standard normal curve to the left of $ z = -1 $ or to the right of $ z = 1 $

To find the total area under the standard normal curve to the left of $ z = -1 $ or to the right of $ z = 1 $, we use the properties of the standard normal distribution. The area to the left of $ z = -1 $ is the same as the area to the right of $ z = 1 $ due to symmetry. The total area is given as 0.3174.

Step 2: Determine the total area under the standard normal curve to the left of $ z = -1.59 $ or to the right of $ z = 2.59 $

To find the total area under the standard normal curve to the left of $ z = -1.59 $ or to the right of $ z = 2.59 $, we look up these values in the standard normal distribution table. The area to the left of $ z = -1.59 $ and the area to the right of $ z = 2.59 $ are added together to find the total area.

Final Answer

{"axisType": 3, "coordSystem": {"xmin": -3, "xmax": 3, "ymin": -2, "ymax": 2}, "commands": ["y = (1/sqrt(2_pi))_exp(-0.5*x**2)"], "latex_expressions": ["$y = \\frac{1}{\\sqrt{2\\pi}}e^{-0.5x^2}$"]}

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