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There were 49.7 million people with some type of long-lasting condition or disability living in the United States in 2000. This represented 19.3 percent of the majority of civilians aged five and over (http://factfinder.census.gov). A sample of 1000 persons is selected at random. Use normal approximation. Round the answers to four decimal places (e.g. 98.7654). (a) Approximate the probability that more than 200 persons in the sample have a disability. 0.2743 (b) Approximate the probability that between 180 and 300 people in the sample have a disability.

There were 49.7 million people with some type of long-lasting condition or disability living in the United States in 2000. This represented 19.3 percent of the majority of civilians aged five and over (http://factfinder.census.gov). A sample of 1000 persons is selected at random. Use normal approximation. Round the answers to four decimal places (e.g. 98.7654). (a) Approximate the probability that more than 200 persons in the sample have a disability. 0.2743 (b) Approximate the probability that between 180 and 300 people in the sample have a disability.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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### Understanding Probability for Long-Lasting Conditions or Disabilities Based on data from the United States Census in 2000, there were 49.7 million people with some type of long-lasting condition or disability. This group represented 19.3 percent of the majority of civilians aged five and over. To explore these statistics further, let's consider a hypothetical scenario where a sample of 1,000 persons is selected at random. Using normal approximation, we will address two specific probabilities related to this sample. Note that all answers are rounded to four decimal places (e.g., 98.7654). #### (a) Probability of More than 200 Persons with a Disability We are interested in approximating the probability that more than 200 people in the sample have a disability. Based on the calculations done, this probability is: \[ \boxed{0.2743} \] #### (b) Probability of Between 180 and 300 Persons with a Disability In this part, we approximate the probability that the number of people with a disability in the sample falls between 180 and 300. After performing the necessary calculations, we find that this probability is: \[ \boxed{0.8413} \] These probabilities illustrate the likelihood of certain outcomes within a given sample, based on the larger population data from the 2000 Census. Understanding these probabilities can help in various fields, such as public health planning, resource allocation, and policy making. For further exploration and detailed methodology, please refer to resources on probability theory and the normal approximation to the binomial distribution.
Transcribed Image Text:### Understanding Probability for Long-Lasting Conditions or Disabilities Based on data from the United States Census in 2000, there were 49.7 million people with some type of long-lasting condition or disability. This group represented 19.3 percent of the majority of civilians aged five and over. To explore these statistics further, let's consider a hypothetical scenario where a sample of 1,000 persons is selected at random. Using normal approximation, we will address two specific probabilities related to this sample. Note that all answers are rounded to four decimal places (e.g., 98.7654). #### (a) Probability of More than 200 Persons with a Disability We are interested in approximating the probability that more than 200 people in the sample have a disability. Based on the calculations done, this probability is: \[ \boxed{0.2743} \] #### (b) Probability of Between 180 and 300 Persons with a Disability In this part, we approximate the probability that the number of people with a disability in the sample falls between 180 and 300. After performing the necessary calculations, we find that this probability is: \[ \boxed{0.8413} \] These probabilities illustrate the likelihood of certain outcomes within a given sample, based on the larger population data from the 2000 Census. Understanding these probabilities can help in various fields, such as public health planning, resource allocation, and policy making. For further exploration and detailed methodology, please refer to resources on probability theory and the normal approximation to the binomial distribution.
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