**Title: Statistical Analysis of Female Heart Transplant Survival Rates****Introduction**:Understanding the survival rates of female heart transplant patients is crucial for medical professionals and researchers. This educational module will explore the probability that a sample proportion of patients surviving for at least 3 years will be less than a given percentage. **Problem Statement**:Approximately 77% of all female heart transplant patients will survive for at least 3 years. From a randomly selected sample of 70 female heart transplant patients, what is the probability that the sample proportion surviving for at least 3 years will be less than 69%? Assume the sampling distribution of sample proportions follows a normal distribution. **Parameters**:- Population proportion (p): 77% or 0.77- Sample size (n): 70- Target sample proportion: 69% or 0.69**Calculations**:1. **Mean of the Sample Proportion**: The mean of the sample proportion is equal to the population proportion, which is: \[ \mu_p = p = 0.77 \] 2. **Standard Deviation of the Sample Proportion**: The standard deviation of the sample proportion is calculated using the formula: \[ \sigma_p = \sqrt{\frac{pq}{n}} \] where: - $ p = 0.77 $ - $ q = 1 - p = 0.23 $ - $ n = 70 $ Therefore, \[ \sigma_p = \sqrt{\frac{0.77 \times 0.23}{70}} = \sqrt{\frac{0.1771}{70}} = \sqrt{0.00253} \approx 0.0503 \]3. **Z-Score Calculation**: To find the probability that the sample proportion is less than 69%, we calculate the z-score using: \[ Z = \frac{\hat{p} - \mu_p}{\sigma_p} \] where: - $ \hat{p} = 0.69 $ - $ \mu_p = 0.77 $ - $ \sigma_p = 0.0503 $ Thus, \[ Z = \frac{0.69 - 0.77}{0

About 77% of all female heart transplant patients will survive for at least 3 years. Seventy female heart transplant patients are randomly selected. What is the probability that the sample proportion surviving for at least 3 years will be less than 69%? Assume the sampling distribution of sample proportions is a normal pq distribution. The mean of the sample proportion is equal to the population proportion and the standard deviation is equal to The probability that the sample proportion surviving for at least 3 years will be less than 69% is (Round to four decimal places as needed.)

About 77% of all female heart transplant patients will survive for at least 3 years. Seventy female heart transplant patients are randomly selected. What is the probability that the sample proportion surviving for at least 3 years will be less than 69%? Assume the sampling distribution of sample proportions is a normal pq distribution. The mean of the sample proportion is equal to the population proportion and the standard deviation is equal to The probability that the sample proportion surviving for at least 3 years will be less than 69% is (Round to four decimal places as needed.)

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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