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: Save \& Exit Practice Lesson: 6.2 The Standard Normal Distribut... 3/15 0 Correct Question 4 of 15. Step 1 of 1 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 need 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 $.

Step 2: Use the Standard Normal Distribution Table

The standard normal distribution table (or Z-table) provides the area to the left of a given $ z $-score. We will use this table to find the areas for $ z_1 = -2.575 $ and $ z_2 = 2.575 $.

Step 3: Find the Area to the Left of $ z_1 = -2.575 $

Using the Z-table, the area to the left of $ z_1 = -2.575 $ is approximately 0.0050.

Step 4: Find the Area to the Right of $ z_2 = 2.575 $

The area to the right of a $ z $-score is $ 1 $ minus the area to the left. For $ z_2 = 2.575 $, the area to the left is also approximately 0.9950. Therefore, the area to the right is:

\[ 1 - 0.9950 = 0.0050 \]

Step 5: Calculate the Total Area

The total area is the sum of the areas to the left of $ z_1 $ and to the right of $ z_2 $:

\[ 0.0050 + 0.0050 = 0.0100 \]