Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the z-score of a man 79.5 inches tall. (to 4 decimal places) エ-ド Use the formula Z = where u is the mean, o is the standard deviation, and x is the man's height.
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.
![## Calculating the Z-Score
### Problem Statement:
Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the z-score of a man 79.5 inches tall. (to 4 decimal places)
### Formula for Z-Score:
\[ Z = \frac{x - \mu}{\sigma} \]
Where:
- \(\mu\) is the mean,
- \(\sigma\) is the standard deviation,
- \(x\) is the man's height.
### Example Calculation:
Given:
- Mean (\(\mu\)) = 69.0 inches
- Standard Deviation (\(\sigma\)) = 2.8 inches
- Man's Height (\(x\)) = 79.5 inches
#### Steps:
1. Subtract the mean from the man's height.
2. Divide the result by the standard deviation.
3. Round the result to four decimal places.
### Detailed Calculation:
1. \( x - \mu = 79.5 - 69.0 = 10.5 \)
2. \( \frac{10.5}{2.8} \approx 3.7500 \)
Thus, the z-score is approximately \( 3.7500 \).
By understanding and applying the above steps, students can calculate the z-score for any given set of data points. This type of calculation is essential for standardizing different measurements and understanding their positions within a normal distribution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa2daf47f-1d43-4c0e-a218-05866800687b%2Fd55d5053-33ca-4471-bcb0-f36c3bc2d1e0%2Fa41z8ge.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
