Question

(b) find the area under the normal curve to the left of \\(z = -1.57\\) plus the area under the normal curve to the right of \\(z = 2.57\\).

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

Explanation:

⚡ Using what you learned: normal distribution

Step 1: Find the area to the left of \( z = -1.57 \)

Using a standard normal distribution table (z-table):

$$ P(Z < -1.57) = 0.0582 $$

Step 2: Find the area to the right of \( z = 2.57 \)

Using the complement rule:

$$ P(Z > 2.57) = 1 - P(Z < 2.57) $$

$$ P(Z > 2.57) = 1 - 0.9949 = 0.0051 $$

Step 3: Calculate the combined area

$$ \text{Combined Area} = 0.0582 + 0.0051 = 0.0633 $$

Answer:

0.0633