According to a study, the proportion of people who are satisfied with the way things are going in their lives is 0.80. Suppose that a random sample of 100 people is obtained.
According to a study, the proportion of people who are satisfied with the way things are going in their lives is 0.80. Suppose that a random sample of 100 people is obtained.
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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According to a study, the proportion of people who are satisfied with the way things are going in their lives is 0.80. Suppose that a random sample of 100 people is obtained.
- [Click here to view the standard normal distribution table (page 2).](#)
**Questions:**
**(c) Describe the sampling distribution of \(\hat{p}\),** the proportion of people who are satisfied with the way things are going in their life. Be sure to verify the model requirements.
- Since the sample size is 100, which is no less than 5% of the population size and \( np(1 - p) = \) [Blank for entry] \( > 10 \), the distribution of \(\hat{p}\) is approximately normal with \( \mu_{\hat{p}} = 0.80 \) and \( \sigma_{\hat{p}} = 0.040 \).
(Round to three decimal places as needed.)
**(d) In the sample obtained in part (a), what is the probability that the proportion of people who are satisfied with the way things are going in their life exceeds 0.83?**
- The probability that the proportion who are satisfied with the way things are going in their life exceeds 0.83 is [Blank for entry].
(Round to four decimal places as needed.)
**(e) Using the distribution from part (c),** would it be unusual for a survey of 100 people to reveal that 72 or fewer people in the sample are satisfied with their lives?
- The probability that 72 or fewer people in the sample are satisfied is [Blank for entry], which [Dropdown for selection] unusual because this probability [Blank for entry] less than [Blank for entry]%.
(Round to four decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04eb1062-54d0-416c-ad3c-f2b55c6eff31%2Ff7c40df6-ceda-4696-8eb1-f33faeed4c85%2Fcsaw2gi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:According to a study, the proportion of people who are satisfied with the way things are going in their lives is 0.80. Suppose that a random sample of 100 people is obtained. Complete parts (a) through (e) below.
**Links to Standard Normal Distribution Tables:**
- [Click here to view the standard normal distribution table (page 1).](#)
- [Click here to view the standard normal distribution table (page 2).](#)
**Questions:**
**(c) Describe the sampling distribution of \(\hat{p}\),** the proportion of people who are satisfied with the way things are going in their life. Be sure to verify the model requirements.
- Since the sample size is 100, which is no less than 5% of the population size and \( np(1 - p) = \) [Blank for entry] \( > 10 \), the distribution of \(\hat{p}\) is approximately normal with \( \mu_{\hat{p}} = 0.80 \) and \( \sigma_{\hat{p}} = 0.040 \).
(Round to three decimal places as needed.)
**(d) In the sample obtained in part (a), what is the probability that the proportion of people who are satisfied with the way things are going in their life exceeds 0.83?**
- The probability that the proportion who are satisfied with the way things are going in their life exceeds 0.83 is [Blank for entry].
(Round to four decimal places as needed.)
**(e) Using the distribution from part (c),** would it be unusual for a survey of 100 people to reveal that 72 or fewer people in the sample are satisfied with their lives?
- The probability that 72 or fewer people in the sample are satisfied is [Blank for entry], which [Dropdown for selection] unusual because this probability [Blank for entry] less than [Blank for entry]%.
(Round to four decimal places as needed.)
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