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.

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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.
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.)
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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