Jolyn scores an average of 28 points per basketball game, and her points per basketball game are normally distributed. Suppose Jolyn scores 52 points in a game, and this value has a z-score of 4. What is the standard deviation? Do not include the units in your answer. For example, if you found that the standard deviation was 10 points, you would enter 10.
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:**
Jolyn scores an average of 28 points per basketball game, and her points per basketball game are normally distributed. Suppose Jolyn scores 52 points in a game, and this value has a z-score of 4. What is the standard deviation? Do not include the units in your answer. For example, if you found that the standard deviation was 10 points, you would enter 10.
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**Note:**
To calculate the standard deviation, use the formula for a z-score:
\[ z = \frac{(X - \mu)}{\sigma} \]
Where:
- \( z \) is the z-score,
- \( X \) is the value of interest (52 points),
- \( \mu \) is the mean (28 points),
- \( \sigma \) is the standard deviation.
Rearrange the formula to solve for \( \sigma \):
\[ \sigma = \frac{(X - \mu)}{z} \]
Substitute the values given to find the standard deviation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff8a3a9a6-89c8-4a2c-bdfb-160e1d96aa12%2F64b40d9b-efc4-4cc7-9bae-0f34e89d2709%2F9nda3p.jpeg&w=3840&q=75)
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