Question

determine the total area under the standard normal curve in parts (a) through (c) below.

click the icon to view a table of areas under the normal curve.

(a) find the area under the normal curve to the left of (z = -3) plus the area under the normal curve to the right of (z = 3).

the combined area is
(round to four decimal places as needed.)

Explanation:

⚡ Using what you learned: normal distribution

Step 1: Find the area to the left of \( z = -3 \)

Using a standard normal distribution table:

$$ P(Z < -3.00) = 0.0013 $$

Step 2: Find the area to the right of \( z = 3 \)

By symmetry of the normal curve:

$$ P(Z > 3.00) = P(Z < -3.00) = 0.0013 $$

Alternatively, using the complement rule:

$$ P(Z > 3.00) = 1 - P(Z < 3.00) = 1 - 0.9987 = 0.0013 $$

Step 3: Calculate the combined area

Sum the two tail areas:

$$ \text{Combined Area} = 0.0013 + 0.0013 = 0.0026 $$

Answer:

0.0026