Suppose a simple random sample of size n equals 1000 is obtained from a population whose size is N equals 2 comma 000 comma 000 and whose population proportion with a specified characteristic is p equals 0.75. Complete parts (a) through (c) below. 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 = 0.75 $. Complete parts (a) through (c) below.(a) Describe the sampling distribution of $ \hat{p} $.- Option A: Approximately normal, $ \mu_{\hat{p}} = 0.75 $ and $ \sigma_{\hat{p}} \approx 0.0137 $- Option B: Approximately normal, $ \mu_{\hat{p}} = 0.75 $ and $ \sigma_{\hat{p}} \approx 0.0002 $- Option C: Approximately normal, $ \mu_{\hat{p}} = 0.75 $ and $ \sigma_{\hat{p}} \approx 0.0003 $(b) What is the probability of obtaining $ x = 780 $ or more individuals with the characteristic?\[ P(x \geq 780) = \_\_\_\_ \] (Round to four decimal places as needed.)(c) What is the probability of obtaining $ x = 710 $ or fewer individuals with the characteristic?\[ P(x \leq 710) = \_\_\_\_ \] (Round to four decimal places as needed.)

The sample size is 1,000. Here, p= 0.75.

Answered: Suppose a simple random sample of…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

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Suppose a simple random sample of size n equals 1000 is obtained from a population whose size is N equals 2 comma 000 comma 000 and whose population proportion with a specified characteristic is p equals 0.75. Complete parts (a) through (c) below.

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 = 0.75 $. Complete parts (a) through (c) below.

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

- Option A: Approximately normal, $ \mu_{\hat{p}} = 0.75 $ and $ \sigma_{\hat{p}} \approx 0.0137 $
- Option B: Approximately normal, $ \mu_{\hat{p}} = 0.75 $ and $ \sigma_{\hat{p}} \approx 0.0002 $
- Option C: Approximately normal, $ \mu_{\hat{p}} = 0.75 $ and $ \sigma_{\hat{p}} \approx 0.0003 $

(b) What is the probability of obtaining $ x = 780 $ or more individuals with the characteristic?

\[ P(x \geq 780) = \_\_\_\_ \] (Round to four decimal places as needed.)

(c) What is the probability of obtaining $ x = 710 $ or fewer individuals with the characteristic?

\[ P(x \leq 710) = \_\_\_\_ \] (Round to four decimal places as needed.)

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