Question
Find the area outside the interval between z= -1.18 and z=2.47
Answers
Answer
Find the area under standard normal curve to the left of z=2.32
Answer
Area undead standard curve to the right of z=1.13
Answer
Area under normal standard curve between z= -1.32 and z= 1.43
Answered by
GPT-4o mini
To find the area outside the interval between \( z = -1.18 \) and \( z = 2.47 \), we first need to determine the total area under the standard normal curve, which is equal to 1.
Next, we will find the areas corresponding to those z-scores using the standard normal distribution table or a calculator:
1. **Find the area to the left of \( z = -1.18 \)**:
Using a standard normal distribution table, we find:
\[
P(Z < -1.18) \approx 0.1190
\]
2. **Find the area to the left of \( z = 2.47 \)**:
Using a standard normal distribution table, we find:
\[
P(Z < 2.47) \approx 0.9934
\]
3. **Find the area between \( z = -1.18 \) and \( z = 2.47 \)**:
We can calculate this area by subtracting the area to the left of \( z = -1.18 \) from the area to the left of \( z = 2.47 \):
\[
P(-1.18 < Z < 2.47) = P(Z < 2.47) - P(Z < -1.18) \approx 0.9934 - 0.1190 = 0.8744
\]
4. **Find the area outside the interval**:
The area outside the interval is simply:
\[
P(Z < -1.18) + P(Z > 2.47) = P(Z < -1.18) + (1 - P(Z < 2.47))
\]
\[
= 0.1190 + (1 - 0.9934) \approx 0.1190 + 0.0066 = 0.1256
\]
Therefore, the area outside the interval between \( z = -1.18 \) and \( z = 2.47 \) is approximately \( \mathbf{0.1256} \).
Next, we will find the areas corresponding to those z-scores using the standard normal distribution table or a calculator:
1. **Find the area to the left of \( z = -1.18 \)**:
Using a standard normal distribution table, we find:
\[
P(Z < -1.18) \approx 0.1190
\]
2. **Find the area to the left of \( z = 2.47 \)**:
Using a standard normal distribution table, we find:
\[
P(Z < 2.47) \approx 0.9934
\]
3. **Find the area between \( z = -1.18 \) and \( z = 2.47 \)**:
We can calculate this area by subtracting the area to the left of \( z = -1.18 \) from the area to the left of \( z = 2.47 \):
\[
P(-1.18 < Z < 2.47) = P(Z < 2.47) - P(Z < -1.18) \approx 0.9934 - 0.1190 = 0.8744
\]
4. **Find the area outside the interval**:
The area outside the interval is simply:
\[
P(Z < -1.18) + P(Z > 2.47) = P(Z < -1.18) + (1 - P(Z < 2.47))
\]
\[
= 0.1190 + (1 - 0.9934) \approx 0.1190 + 0.0066 = 0.1256
\]
Therefore, the area outside the interval between \( z = -1.18 \) and \( z = 2.47 \) is approximately \( \mathbf{0.1256} \).
Answered by
GPT-4o mini
To find the area under the standard normal curve to the left of \( z = 2.32 \), we can look up the value of \( P(Z < 2.32) \) using the standard normal distribution table or a calculator.
Using the standard normal distribution table, we find:
\[
P(Z < 2.32) \approx 0.9898
\]
Therefore, the area under the standard normal curve to the left of \( z = 2.32 \) is approximately **0.9898**. This means that about 98.98% of the data falls below a z-score of 2.32 in a standard normal distribution.
Using the standard normal distribution table, we find:
\[
P(Z < 2.32) \approx 0.9898
\]
Therefore, the area under the standard normal curve to the left of \( z = 2.32 \) is approximately **0.9898**. This means that about 98.98% of the data falls below a z-score of 2.32 in a standard normal distribution.
Answered by
GPT-4o mini
To find the area under the standard normal curve to the right of \( z = 1.13 \), we can use the following formula:
\[
P(Z > z) = 1 - P(Z < z)
\]
First, we need to determine \( P(Z < 1.13) \). Using a standard normal distribution table or calculator, we find:
\[
P(Z < 1.13) \approx 0.8708
\]
Now, we can calculate the area to the right of \( z = 1.13 \):
\[
P(Z > 1.13) = 1 - P(Z < 1.13) = 1 - 0.8708 = 0.1292
\]
Therefore, the area under the standard normal curve to the right of \( z = 1.13 \) is approximately **0.1292**.
\[
P(Z > z) = 1 - P(Z < z)
\]
First, we need to determine \( P(Z < 1.13) \). Using a standard normal distribution table or calculator, we find:
\[
P(Z < 1.13) \approx 0.8708
\]
Now, we can calculate the area to the right of \( z = 1.13 \):
\[
P(Z > 1.13) = 1 - P(Z < 1.13) = 1 - 0.8708 = 0.1292
\]
Therefore, the area under the standard normal curve to the right of \( z = 1.13 \) is approximately **0.1292**.
Answered by
GPT-4o mini
To find the area under the standard normal curve between \( z = -1.32 \) and \( z = 1.43 \), we will calculate the areas corresponding to these z-scores and then find the difference between them.
1. **Find the area to the left of \( z = -1.32 \)**:
Using a standard normal distribution table or calculator:
\[
P(Z < -1.32) \approx 0.0934
\]
2. **Find the area to the left of \( z = 1.43 \)**:
Using a standard normal distribution table or calculator:
\[
P(Z < 1.43) \approx 0.9236
\]
3. **Find the area between \( z = -1.32 \) and \( z = 1.43 \)**:
We can find this area by subtracting the area to the left of \( z = -1.32 \) from the area to the left of \( z = 1.43 \):
\[
P(-1.32 < Z < 1.43) = P(Z < 1.43) - P(Z < -1.32)
\]
\[
= 0.9236 - 0.0934 = 0.8302
\]
Therefore, the area under the standard normal curve between \( z = -1.32 \) and \( z = 1.43 \) is approximately **0.8302**.
1. **Find the area to the left of \( z = -1.32 \)**:
Using a standard normal distribution table or calculator:
\[
P(Z < -1.32) \approx 0.0934
\]
2. **Find the area to the left of \( z = 1.43 \)**:
Using a standard normal distribution table or calculator:
\[
P(Z < 1.43) \approx 0.9236
\]
3. **Find the area between \( z = -1.32 \) and \( z = 1.43 \)**:
We can find this area by subtracting the area to the left of \( z = -1.32 \) from the area to the left of \( z = 1.43 \):
\[
P(-1.32 < Z < 1.43) = P(Z < 1.43) - P(Z < -1.32)
\]
\[
= 0.9236 - 0.0934 = 0.8302
\]
Therefore, the area under the standard normal curve between \( z = -1.32 \) and \( z = 1.43 \) is approximately **0.8302**.
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