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In 2020, the Census Bureau listed Frisco, Texas as the fastest-growing city in the nation. In fact, 42% of Frisco homewoners moved into their homes within the last 10 years. A random sample of size 74 was obtained. Let ô be the proportion of the sample that moved into their homes within the last 10 years. 1. Use the Central Limit Theorem (np>10 and n(1-p)>10 ) to describe the probability distribution of ô and state its parameters μ and op: (Round the answers to 4 decimal places) p (Hp = ор 2. Find the probability that more than 51% of the sample moved into their homes within the last 10 years. (Round the answer to 4 decimal places) N =

In 2020, the Census Bureau listed Frisco, Texas as the fastest-growing city in the nation. In fact, 42% of Frisco homewoners moved into their homes within the last 10 years. A random sample of size 74 was obtained. Let ô be the proportion of the sample that moved into their homes within the last 10 years. 1. Use the Central Limit Theorem (np>10 and n(1-p)>10 ) to describe the probability distribution of ô and state its parameters μ and op: (Round the answers to 4 decimal places) p (Hp = ор 2. Find the probability that more than 51% of the sample moved into their homes within the last 10 years. (Round the answer to 4 decimal places) N =

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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In 2020, the Census Bureau listed Frisco, Texas as the fastest-growing city in the nation. In fact, 42% of Frisco homeowners moved into their homes within the last 10 years. A random sample of size 74 was obtained. Let \( \hat{p} \) be the proportion of the sample that moved into their homes within the last 10 years. 1. Use the Central Limit Theorem \(( np > 10 \text{ and } n(1-p) > 10 )\) to describe the probability distribution of \( \hat{p} \) and state its parameters \( \mu_{\hat{p}} \) and \( \sigma_{\hat{p}} \): (Round the answers to 4 decimal places) \[ \hat{p} \sim N \left( \mu_{\hat{p}} = \, \_\_\_\_ \, , \sigma_{\hat{p}} = \, \_\_\_\_ \right) \] 2. Find the probability that more than 51% of the sample moved into their homes within the last 10 years. \[ \_\_\_\_ \] (Round the answer to 4 decimal places)
Transcribed Image Text:In 2020, the Census Bureau listed Frisco, Texas as the fastest-growing city in the nation. In fact, 42% of Frisco homeowners moved into their homes within the last 10 years. A random sample of size 74 was obtained. Let \( \hat{p} \) be the proportion of the sample that moved into their homes within the last 10 years. 1. Use the Central Limit Theorem \(( np > 10 \text{ and } n(1-p) > 10 )\) to describe the probability distribution of \( \hat{p} \) and state its parameters \( \mu_{\hat{p}} \) and \( \sigma_{\hat{p}} \): (Round the answers to 4 decimal places) \[ \hat{p} \sim N \left( \mu_{\hat{p}} = \, \_\_\_\_ \, , \sigma_{\hat{p}} = \, \_\_\_\_ \right) \] 2. Find the probability that more than 51% of the sample moved into their homes within the last 10 years. \[ \_\_\_\_ \] (Round the answer to 4 decimal places)
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Step 1

Given,n=74p=0.42np=74×0.42=31.08>10and n(1-p)=74(1-0.42)=42.92>10

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