Question
Find the area under the standard normal distribution curve to the right of \( z=-1.07 \). Use 9 The Standard Normal Distribution Table and enter the answer to 4 decimal places. The area to the right of the \( z \) value is T.
Ask by Nguyen Vaughan. in the United States
Mar 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The area to the right of \( z = -1.07 \) is approximately 0.8577.
Solution
1. Recognize that we want \( P(Z > -1.07) \).
2. The standard normal table gives the area to the left of a \( z \)-value, so first find \( P(Z < -1.07) \).
3. By symmetry of the standard normal distribution, we have
\[
P(Z > -1.07) = P(Z < 1.07).
\]
4. Look up \( z = 1.07 \) in the standard normal table. The table gives
\[
P(Z < 1.07) \approx 0.8577.
\]
5. Thus, the area to the right of \( z = -1.07 \) is
\[
P(Z > -1.07) \approx 0.8577.
\]
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Simplify this solution Beyond the Answer
To find the area under the standard normal distribution curve to the right of \( z = -1.07 \), we first need to find the area to the left of this \( z \)-value using the Standard Normal Distribution Table. The table tells us that for \( z = -1.07 \), the area to the left is approximately 0.1423. To get the area to the right, we subtract this value from 1. Thus, the area to the right is calculated as: \[ 1 - 0.1423 = 0.8577 \] So, the area to the right of \( z = -1.07 \) is 0.8577 when rounded to four decimal places. T = 0.8577
