Questions: Find the total of the areas under the standard normal curve to the left of z1=-2.575 and to the right of z2=2.575. Round your answer to four decimal places, if necessary.

Find the total of the areas under the standard normal curve to the left of z1=-2.575 and to the right of z2=2.575. Round your answer to four decimal places, if necessary.

Transcript text: Find the total of the areas under the standard normal curve to the left of $z_{1}=-2.575$ and to the right of $z_{2}=2.575$. Round your answer to four decimal places, if necessary.

Solution

Solution Steps

Step 1: Understand the problem

We are asked to find the total area under the standard normal curve to the left of $ z_{1} = -2.575 $ and to the right of $ z_{2} = 2.575 $. This involves calculating two probabilities and summing them.

Step 2: Calculate the area to the left of $ z_{1} = -2.575 $

Using the standard normal distribution table or a calculator, the area to the left of $ z_{1} = -2.575 $ is: \[ P(Z < -2.575) = 0.0050 \]

Step 3: Calculate the area to the right of $ z_{2} = 2.575 $

The area to the right of $ z_{2} = 2.575 $ is the same as the area to the left of $ z_{1} = -2.575 $ due to the symmetry of the standard normal distribution: \[ P(Z > 2.575) = P(Z < -2.575) = 0.0050 \]

Step 4: Sum the two areas

The total area is the sum of the two probabilities: \[ \text{Total Area} = P(Z < -2.575) + P(Z > 2.575) = 0.0050 + 0.0050 = 0.0100 \]