(a) What percent of the scores are less than 19? (b) Out of 1500 randomly selected scores, about how many would be expected to be greater than 21?
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.
![### Normal Distribution Questions and Visualization
#### Instructions:
Use the normal distribution to the right to answer the questions.
**(a)** What percent of the scores are less than 19?
**(b)** Out of 1500 randomly selected scores, about how many would be expected to be greater than 21?
#### Graph/Diagram Explanation:
To the right, there is a normal distribution graph labeled *Standardized Test Composite Scores*. The horizontal axis represents the scores, and the vertical axis represents the frequency of those scores. The curve shows a typical bell-shaped normal distribution.
Key elements of the graph:
- **Mean (μ):** 20.8
- **Standard Deviation (σ):** 5.1
- There are marked scores at **19** and **21** on the x-axis.
- The area under the curve is divided to show the probability distribution around these scores.
This graph is useful in understanding the proportion of scores that lie within particular ranges. Using the properties of normal distribution, you can determine the percentages and expected counts for various score intervals.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67365948-39ab-434a-aacf-cd60e1ade7b5%2Fd4c75b5b-068f-401c-94da-b738ad9d9325%2F2woymy_processed.png&w=3840&q=75)
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