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LON Survey reported that the proportion of adults with high blood pressure is 0.3. A sample of 38 U.S. adults are chosen A) A new sample of 80 adults is drawn. Find the probability that more than 40% of the people in this Sample have high blood pressure?

LON Survey reported that the proportion of adults with high blood pressure is 0.3. A sample of 38 U.S. adults are chosen A) A new sample of 80 adults is drawn. Find the probability that more than 40% of the people in this Sample have high blood pressure?

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
Problem 1P
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### Survey Report on High Blood Pressure A survey has reported the proportion of adults with high blood pressure is 0.3. A sample of 38 U.S. adults has been chosen. **Question:** A new sample of 80 adults is drawn. Find the probability that more than 40% of the people in this sample have high blood pressure? **Solution:** To solve this problem, you would typically use the normal approximation to the binomial distribution, due to the large sample size. Here's a step-by-step outline of how to approach this problem: 1. **Determine the parameters:** - Proportion of adults with high blood pressure \( p = 0.3 \) - Sample size \( n = 80 \) - Desired proportion to compare: 40% or 0.4 2. **Calculate the mean and standard deviation:** - Mean \( \mu = np = 80 \times 0.3 = 24 \) - Standard deviation \( \sigma = \sqrt{np(1-p)} = \sqrt{80 \times 0.3 \times 0.7} \approx 4.099 \) 3. **Convert the required proportion to a number of successes:** - The threshold proportion is 0.4 - Corresponding number of successes \( X = 0.4 \times 80 = 32 \) 4. **Find the z-score for 32 successes:** - \( Z = \frac{X - \mu}{\sigma} = \frac{32 - 24}{4.099} \approx 1.95 \) 5. **Use standard normal distribution to find the probability:** - Look up the z-score of 1.95 in the standard normal distribution table or use a calculator: - Probability \( P(Z < 1.95) \approx 0.9744 \) - Since we need the probability that the proportion is more than 40%, we use the complement: - \( P(Z > 1.95) = 1 - P(Z < 1.95) = 1 - 0.9744 = 0.0256 \) So, the probability that more than 40% of the people in this sample have high blood pressure is approximately 2.56%.
Transcribed Image Text:### Survey Report on High Blood Pressure A survey has reported the proportion of adults with high blood pressure is 0.3. A sample of 38 U.S. adults has been chosen. **Question:** A new sample of 80 adults is drawn. Find the probability that more than 40% of the people in this sample have high blood pressure? **Solution:** To solve this problem, you would typically use the normal approximation to the binomial distribution, due to the large sample size. Here's a step-by-step outline of how to approach this problem: 1. **Determine the parameters:** - Proportion of adults with high blood pressure \( p = 0.3 \) - Sample size \( n = 80 \) - Desired proportion to compare: 40% or 0.4 2. **Calculate the mean and standard deviation:** - Mean \( \mu = np = 80 \times 0.3 = 24 \) - Standard deviation \( \sigma = \sqrt{np(1-p)} = \sqrt{80 \times 0.3 \times 0.7} \approx 4.099 \) 3. **Convert the required proportion to a number of successes:** - The threshold proportion is 0.4 - Corresponding number of successes \( X = 0.4 \times 80 = 32 \) 4. **Find the z-score for 32 successes:** - \( Z = \frac{X - \mu}{\sigma} = \frac{32 - 24}{4.099} \approx 1.95 \) 5. **Use standard normal distribution to find the probability:** - Look up the z-score of 1.95 in the standard normal distribution table or use a calculator: - Probability \( P(Z < 1.95) \approx 0.9744 \) - Since we need the probability that the proportion is more than 40%, we use the complement: - \( P(Z > 1.95) = 1 - P(Z < 1.95) = 1 - 0.9744 = 0.0256 \) So, the probability that more than 40% of the people in this sample have high blood pressure is approximately 2.56%.
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