Question

determine the area under the standard normal curve that lies to the left of (a) \\(z = -1.07\\), (b) \\(z = 1.66\\), (c) \\(z = -0.06\\), and (d) \\(z = 0.38\\).

Explanation:

⚡ Using what you learned: normal distribution

Step 1: Find the area to the left of \( Z = -1.07 \)

Using a standard normal distribution table (Z-table) for \( Z = -1.07 \):

$$ P(Z < -1.07) = 0.1423 $$

Step 2: Find the area to the left of \( Z = 1.66 \)

Using a standard normal distribution table for \( Z = 1.66 \):

$$ P(Z < 1.66) = 0.9515 $$

Step 3: Find the area to the left of \( Z = -0.06 \)

Using a standard normal distribution table for \( Z = -0.06 \):

$$ P(Z < -0.06) = 0.4761 $$

Step 4: Find the area to the left of \( Z = 0.38 \)

Using a standard normal distribution table for \( Z = 0.38 \):

$$ P(Z < 0.38) = 0.6480 $$

Answer:

(a) \( 0.1423 \)
(b) \( 0.9515 \)
(c) \( 0.4761 \)
(d) \( 0.6480 \)