The residents of two towns both have a mean income of $30,000. Town A has a standard deviation of $2600 and Town B has a standard deviation of $25,000. 21. For Town A, what interval covers the middle 68% of the incomes? 22. For Town A, what interval covers the middle 95% of the incomes? 23. For Town A, what interval covers the middle 99.7% of the incomes?
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.
![The residents of two towns both have a mean income of $30,000.
Town A has a standard deviation of $2600 and Town B has a standard deviation of $25,000.
21. For Town A, what interval covers the middle 68% of the incomes?
22. For Town A, what interval covers the middle 95% of the incomes?
23. For Town A, what interval covers the middle 99.7% of the incomes?
24. For Town B, what interval covers the middle 68% of the incomes?
25. For Town B, what interval covers the middle 95% of the incomes? (okay to have a negative value)
26. For Town B, what interval covers the middle 99.7% of incomes? (okay to have a negative value)
27. Draw the normal density curves for both Town A and Town B on the same axis. Label the towns.
28. Which town has the taller normal density curve?
29. Which town has the wider normal density curve?
30. Explain what this says about the difference in the distribution of incomes in the two towns](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F845a5cbc-9aeb-411a-a0ea-35818b4b64f4%2F485c06a3-e507-4c53-9ef3-b1a46e2ed4ab%2Fcyftbf_processed.jpeg&w=3840&q=75)
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