Find the probabillty using the normal distribution: P(-2.69
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
 and enter the answer to 4 decimal places.**
\[ P(-2.69 < z < 0) =\ \_ \_ \_ \_ \]
### Steps to Solve:
1. **Identify the Z-Scores:**
- Negative Z-score: -2.69
- Zero Z-score: 0
2. **Consult the Standard Normal Distribution Table:**
- Look up the value corresponding to \( z = 0 \) in the table. This should be 0.5 because the area under the curve from the mean (z=0) to the left is exactly half.
- Look up the value corresponding to \( z = -2.69 \) in the table. The table typically gives the cumulative probability from the far left up to the given z-score.
3. **Calculate the Area:**
- The cumulative probability for \( z = -2.69 \) can be directly obtained from the table.
- To find \( P(-2.69 < z < 0) \), subtract the cumulative probability for \( z = -2.69 \) from the cumulative probability for \( z = 0 \) (0.5).
4. **Output the Result:**
- Enter the probability to four decimal places.
### Reference:
- **Standard Normal Distribution Table**: A useful tool for finding the probability associated with a standard normal distribution (bell-curve).
**Note:**
- Values from standard normal tables represent areas (probabilities) under the bell curve. The cumulative area from far left (-∞) to a z-score.
### Check and Submit:
- You can press "Check" to verify your answer or "Save For Later" to continue at a later time.
---
**Final Answer Submission:**
\[ P(-2.69 < z < 0) = \_\_ \_\_ \_\_ \_\_ \]
---
**Reminder: Always cross-check with the Standard Normal Distribution Table for accurate results. This example ensures clarity in navigating through z-scores and interpreting results.**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea0820f3-64e4-4dfd-b401-c1fa00677880%2F58df57b1-6627-45c0-b22a-a02bbb35a2fd%2Fd1et0hl_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
