Suppose a simple random sample of size n= 1000 is obtained from a population whose size is N = 2,000,000 and whose population proportion with a specified characteristic isp=0.55. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. O A. Approximately normal, µn = 0.55 and on z 0.0004 "p O B. Approximately normal, Ha = 0.55 and on 2 0.0157 OC. Approximately normal, µa = 0.55 and on 0.0002 (b) What is the probability of obtaining x = 580 or more individuals with the characteristic? P(x2 580) = (Round to four decimal places as needed.) (c) What is the probability of obtaining x = 530 or fewer individuals with the characteristic? P(xs 530) = |(Round to four decimal places as needed.)

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**Sampling Distribution of Proportion**

Suppose a simple random sample of size \( n = 1000 \) is obtained from a population whose size is \( N = 2,000,000 \) and whose population proportion with a specified characteristic is \( p = 0.55 \). Complete parts (a) through (c) below.

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

- A. Approximately normal, \(\mu_{\hat{p}} = 0.55\) and \(\sigma_{\hat{p}} \approx 0.0004\)

- B. Approximately normal, \(\mu_{\hat{p}} = 0.55\) and \(\sigma_{\hat{p}} \approx 0.0157\)

- C. Approximately normal, \(\mu_{\hat{p}} = 0.55\) and \(\sigma_{\hat{p}} \approx 0.0002\)

**(b) What is the probability of obtaining \( x = 580 \) or more individuals with the characteristic?**

\[ P(x \geq 580) = \text{[ ]} \quad (\text{Round to four decimal places as needed.}) \]

**(c) What is the probability of obtaining \( x = 530 \) or fewer individuals with the characteristic?**

\[ P(x \leq 530) = \text{[ ]} \quad (\text{Round to four decimal places as needed.}) \]
Transcribed Image Text:**Sampling Distribution of Proportion** Suppose a simple random sample of size \( n = 1000 \) is obtained from a population whose size is \( N = 2,000,000 \) and whose population proportion with a specified characteristic is \( p = 0.55 \). Complete parts (a) through (c) below. **(a) Describe the sampling distribution of \(\hat{p}\).** - A. Approximately normal, \(\mu_{\hat{p}} = 0.55\) and \(\sigma_{\hat{p}} \approx 0.0004\) - B. Approximately normal, \(\mu_{\hat{p}} = 0.55\) and \(\sigma_{\hat{p}} \approx 0.0157\) - C. Approximately normal, \(\mu_{\hat{p}} = 0.55\) and \(\sigma_{\hat{p}} \approx 0.0002\) **(b) What is the probability of obtaining \( x = 580 \) or more individuals with the characteristic?** \[ P(x \geq 580) = \text{[ ]} \quad (\text{Round to four decimal places as needed.}) \] **(c) What is the probability of obtaining \( x = 530 \) or fewer individuals with the characteristic?** \[ P(x \leq 530) = \text{[ ]} \quad (\text{Round to four decimal places as needed.}) \]
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