If the mean is seven and the standard deviation is two, what value is three standard deviations to the right of the mean?
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.
![**Question on Standard Deviations**
If the mean is seven and the standard deviation is two, what value is three standard deviations to the right of the mean?
**Explanation:**
To find a value that is a certain number of standard deviations away from the mean, you use the formula:
\[ \text{Value} = \text{Mean} + (\text{Number of Standard Deviations} \times \text{Standard Deviation}) \]
In this case:
- The mean (\( \mu \)) = 7
- The standard deviation (\( \sigma \)) = 2
- The number of standard deviations = 3
Therefore, the calculation is:
\[ \text{Value} = 7 + (3 \times 2) \]
\[ \text{Value} = 7 + 6 \]
\[ \text{Value} = 13 \]
So, three standard deviations to the right of the mean is 13.
There are no graphs or diagrams in the provided image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b7c328d-a0d5-43ae-9018-e0e85deb839d%2F50ae01ad-7734-440a-982a-d53ac104439b%2Fjxg9jfb_processed.jpeg&w=3840&q=75)
Step by step
Solved in 2 steps
