Use the Empirical Rule (68-95-99.7) to identify the interval. The time between infection with the HIV virus and developing AIDS follows a normal distribution with a mean of 8 years and a standard deviation of 2 years. Find the time interval in which 95% of those who have been infected with the HIV virus will develop AIDS. from 4 to 12 years from 5 to 11 years from 2 to 14 years from 3 to 13 years
Use the Empirical Rule (68-95-99.7) to identify the interval. The time between infection with the HIV virus and developing AIDS follows a normal distribution with a mean of 8 years and a standard deviation of 2 years. Find the time interval in which 95% of those who have been infected with the HIV virus will develop AIDS. from 4 to 12 years from 5 to 11 years from 2 to 14 years from 3 to 13 years
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Use the Empirical Rule (68-95-99.7) to identify the interval.**
The time between infection with the HIV virus and developing AIDS follows a normal distribution with a mean of 8 years and a standard deviation of 2 years.
Find the time interval in which 95% of those who have been infected with the HIV virus will develop AIDS.
- ☐ from 4 to 12 years
- ☐ from 5 to 11 years
- ☐ from 2 to 14 years
- ☐ from 3 to 13 years
- ☑ from 6 to 10 years
**Explanation:**
The Empirical Rule states that for a normal distribution:
- 68% of data falls within 1 standard deviation of the mean.
- 95% falls within 2 standard deviations.
- 99.7% falls within 3 standard deviations.
Given a mean of 8 years and a standard deviation of 2 years, 95% of the data falls within 2 standard deviations. Thus, the interval is 8 ± (2 * 2), which equals from 6 to 10 years.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa714d614-78a6-4d97-b2db-18c7cb38b192%2Fa28be72f-1dc3-494d-94a4-ddc44b755859%2Fhj6c26_processed.png&w=3840&q=75)
Transcribed Image Text:**Use the Empirical Rule (68-95-99.7) to identify the interval.**
The time between infection with the HIV virus and developing AIDS follows a normal distribution with a mean of 8 years and a standard deviation of 2 years.
Find the time interval in which 95% of those who have been infected with the HIV virus will develop AIDS.
- ☐ from 4 to 12 years
- ☐ from 5 to 11 years
- ☐ from 2 to 14 years
- ☐ from 3 to 13 years
- ☑ from 6 to 10 years
**Explanation:**
The Empirical Rule states that for a normal distribution:
- 68% of data falls within 1 standard deviation of the mean.
- 95% falls within 2 standard deviations.
- 99.7% falls within 3 standard deviations.
Given a mean of 8 years and a standard deviation of 2 years, 95% of the data falls within 2 standard deviations. Thus, the interval is 8 ± (2 * 2), which equals from 6 to 10 years.
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