**Educational Transcript: Sampling Distribution and Probability Calculation****Problem Statement:**Suppose a simple random sample of size $ n = 1000 $ is obtained from a population whose size is $ N = 1,500,000 $ and whose population proportion with a specified characteristic is $ p = 0.54 $. Complete parts (a) through (c) below.**(a) Describe the sampling distribution of $\hat{p}$:**- **Option A:** Approximately normal, $\mu_{\hat{p}} = 0.54$ and $\sigma_{\hat{p}} \approx 0.0002$- **Option B:** Approximately normal, $\mu_{\hat{p}} = 0.54$ and $\sigma_{\hat{p}} \approx 0.0004$- **Option C:** Approximately normal, $\mu_{\hat{p}} = 0.54$ and $\sigma_{\hat{p}} \approx 0.0158$**(b) Probability Calculation of Obtaining $ x = 570 $ or More Individuals with the Characteristic:**\[ P(x \geq 570) = \_\_\_\_ \] - *(Round to four decimal places as needed.)***(c) Probability Calculation of Obtaining $ x = 520 $ or Fewer Individuals with the Characteristic:**\[ P(x \leq 520) = \_\_\_\_ \]- *(Round to four decimal places as needed.)***Explanation:**The problem involves determining the properties of a sampling distribution and calculating probabilities based on this distribution. You are given options for the characteristics of the distribution (mean and standard deviation) and must select the correct one. Then you use this distribution to calculate probabilities for specific sample outcomes.

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Suppose a simple random sample of size n = 1000 is obtained from a population whose size is N= 1,500,000 and whose population proportion with a specified characteristic is p= 0.54. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. O A. Approximately normal, Ha = 0.54 and o, 0.0002 O B. Approximately normal, H. = 0.54 and o. s0.0004 OC. Approximately normal, Ha = 0.54 and oa 0.0158 "P (b) What is the probability of obtaining x = 570 or more individuals with the characteristic? P(x2 570) = (Round to four decimal places as needed.) (c) What is the probability of obtaining x = 520 or fewer individuals with the characteristic? P(xs 520) = (Round to four decimal places as needed.)

Suppose a simple random sample of size n = 1000 is obtained from a population whose size is N= 1,500,000 and whose population proportion with a specified characteristic is p= 0.54. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. O A. Approximately normal, Ha = 0.54 and o, 0.0002 O B. Approximately normal, H. = 0.54 and o. s0.0004 OC. Approximately normal, Ha = 0.54 and oa 0.0158 "P (b) What is the probability of obtaining x = 570 or more individuals with the characteristic? P(x2 570) = (Round to four decimal places as needed.) (c) What is the probability of obtaining x = 520 or fewer individuals with the characteristic? P(xs 520) = (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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**Educational Transcript: Sampling Distribution and Probability Calculation**

**Problem Statement:**
Suppose a simple random sample of size $ n = 1000 $ is obtained from a population whose size is $ N = 1,500,000 $ and whose population proportion with a specified characteristic is $ p = 0.54 $. Complete parts (a) through (c) below.

**(a) Describe the sampling distribution of $\hat{p}$:**

- **Option A:** Approximately normal, $\mu_{\hat{p}} = 0.54$ and $\sigma_{\hat{p}} \approx 0.0002$
- **Option B:** Approximately normal, $\mu_{\hat{p}} = 0.54$ and $\sigma_{\hat{p}} \approx 0.0004$
- **Option C:** Approximately normal, $\mu_{\hat{p}} = 0.54$ and $\sigma_{\hat{p}} \approx 0.0158$

**(b) Probability Calculation of Obtaining $ x = 570 $ or More Individuals with the Characteristic:**

\[ P(x \geq 570) = \_\_\_\_ \]
- *(Round to four decimal places as needed.)*

**(c) Probability Calculation of Obtaining $ x = 520 $ or Fewer Individuals with the Characteristic:**

\[ P(x \leq 520) = \_\_\_\_ \]
- *(Round to four decimal places as needed.)*

**Explanation:**
The problem involves determining the properties of a sampling distribution and calculating probabilities based on this distribution. You are given options for the characteristics of the distribution (mean and standard deviation) and must select the correct one. Then you use this distribution to calculate probabilities for specific sample outcomes.

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