Question

determine the area under the standard normal curve that lies to the right of (a) \\(z = -1.58\\), (b) \\(z = -0.52\\), (c) \\(z = -0.27\\), and (d) \\(z = 1.07\\).

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

(a) the area to the right of \\(z = -1.58\\) is
(round to four decimal places as needed.)

(b) the area to the right of \\(z = -0.52\\) is
(round to four decimal places as needed.)

(c) the area to the right of \\(z = -0.27\\) is
(round to four decimal places as needed.)

(d) the area to the right of \\(z = 1.07\\) is
(round to four decimal places as needed.)

Explanation:

⚡ Using what you learned: normal distribution

Step 1: Area to the right of \( Z = -1.58 \)

Using a standard normal distribution table, find the cumulative area to the left of \( Z = -1.58 \):

$$ P(Z < -1.58) = 0.0571 $$

Subtract this value from 1 to find the area to the right:

$$ P(Z > -1.58) = 1 - 0.0571 = 0.9429 $$

Step 2: Area to the right of \( Z = -0.52 \)

Find the cumulative area to the left of \( Z = -0.52 \):

$$ P(Z < -0.52) = 0.3015 $$

Subtract this value from 1 to find the area to the right:

$$ P(Z > -0.52) = 1 - 0.3015 = 0.6985 $$

Step 3: Area to the right of \( Z = -0.27 \)

Find the cumulative area to the left of \( Z = -0.27 \):

$$ P(Z < -0.27) = 0.3936 $$

Subtract this value from 1 to find the area to the right:

$$ P(Z > -0.27) = 1 - 0.3936 = 0.6064 $$

Step 4: Area to the right of \( Z = 1.07 \)

Find the cumulative area to the left of \( Z = 1.07 \):

$$ P(Z < 1.07) = 0.8577 $$

Subtract this value from 1 to find the area to the right:

$$ P(Z > 1.07) = 1 - 0.8577 = 0.1423 $$

Answer:

(a) The area to the right of \( Z = -1.58 \) is 0.9429
(b) The area to the right of \( Z = -0.52 \) is 0.6985
(c) The area to the right of \( Z = -0.27 \) is 0.6064
(d) The area to the right of \( Z = 1.07 \) is 0.1423