The equation for a general normal curve with mean u and standard deviation o is e-(x - w)²/(202) y = oV 27 Calculate values for x = 70, 80, ..., 120, 130 where u = 100 and o = 20. Note that setting u = 0 and o = 1 in this equation gives the equation for the standard normal curve. (Round your answers to four decimal places.) X = 70 x 80 X = 90 x = 100 x = 110 X = 120 20
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.
![## General Normal Curve Calculation
### Understanding the Normal Curve Equation
The equation for a general normal curve with mean \( \mu \) and standard deviation \( \sigma \) is given by:
\[ y = \frac{e^{-\frac{(x - \mu)^2}{2\sigma^2}}}{\sigma \sqrt{2\pi}} \]
### Calculation Example
Calculate values for \( x = 70, 80, 90, \ldots, 120, 130 \) where \( \mu = 100 \) and \( \sigma = 20 \).
Note that setting \( \mu = 0 \) and \( \sigma = 1 \) in the above equation gives the equation for the standard normal curve. (Round your answers to four decimal places.)
- \( x = 70 \) : [Input Box]
- \( x = 80 \) : [Input Box]
- \( x = 90 \) : [Input Box]
- \( x = 100 \) : [Input Box]
- \( x = 110 \) : [Input Box]
- \( x = 120 \) : [Input Box]
- \( x = 130 \) : [Input Box]
### Steps to Calculate
1. **Insert the values:** For each \( x \) value, substitute \( x \), \( \mu \), and \( \sigma \) into the equation.
2. **Evaluate the exponential term:** Calculate \( -\frac{(x - \mu)^2}{2\sigma^2} \).
3. **Calculate:** Evaluate the exponent \( e \) raised to the result from step 2.
4. **Divide:** Divide by \( \sigma \sqrt{2\pi} \).
5. **Round:** Round the final result to four decimal places.
By following these steps, you can calculate the probability density for any specific value of \( x \) on this normal distribution.
Note: There are no graphs or diagrams included in this text.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F373e3400-461c-4f07-afaf-9f92fd60170d%2Ffa30e619-f2b2-46b9-80c6-917058a9c267%2Fidimi4v_processed.png&w=3840&q=75)
Step by step
Solved in 2 steps with 1 images
