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. (a) Determine the total area under the standard normal curve to the left of z=-2 or to the right of z=2. Draw a standard normal curve and shade the area that is to be found. Choose the correct graph below. The total area under the standard normal curve to the left of z=-2 or to the right of z=2 is (Round to four decimal places as needed.)

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.
(a) Determine the total area under the standard normal curve to the left of z=-2 or to the right of z=2.

Draw a standard normal curve and shade the area that is to be found. Choose the correct graph below.

The total area under the standard normal curve to the left of z=-2 or to the right of z=2 is (Round to four decimal places as needed.)

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. (a) Determine the total area under the standard normal curve to the left of $z=-2$ or to the right of $z=2$. Draw a standard normal curve and shade the area that is to be found. Choose the correct graph below. The total area under the standard normal curve to the left of $z=-2$ or to the right of $z=2$ is (Round to four decimal places as needed.)

Solution

Solution Steps

Step 1: Determine the area to the left of $ z = -2 $

The area to the left of $ z = -2 $ can be found using the standard normal distribution table. The cumulative probability for $ z = -2 $ is approximately 0.0228.

Step 2: Determine the area to the right of $ z = 2 $

The area to the right of $ z = 2 $ is the complement of the cumulative probability for $ z = 2 $. The cumulative probability for $ z = 2 $ is approximately 0.9772, so the area to the right is $ 1 - 0.9772 = 0.0228 $.

Step 3: Calculate the total area

The total area under the standard normal curve to the left of $ z = -2 $ or to the right of $ z = 2 $ is the sum of the two areas calculated above: \[ 0.0228 + 0.0228 = 0.0456 \]

Final Answer

The total area under the standard normal curve to the left of $ z = -2 $ or to the right of $ z=2 $ is 0.0456.

{"axisType": 3, "coordSystem": {"xmin": -3, "xmax": 3, "ymin": -0.1, "ymax": 0.5}, "commands": ["y = (1/sqrt(2_pi))_exp(-0.5*x**2)"], "latex_expressions": ["$y = \\frac{1}{\\sqrt{2\\pi}}e^{-0.5x^2}$"]}

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!