Suppose a simple random sample of size n = 50 is obtained from a population whose size is N = 10,000 and whose population proportion with a specified characteristic is p = 0.4. Complete parts (a) through (c) below. ..... (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. O A. Not normal because ns0.05N and np(1 - p)< 10. O B. Approximately normal because ns0.05N and np(1-p) < 10. OC. Not normal because ns0.05N and np(1-p) 2 10. O D. Approximately normal because ns0.05N and np(1 - p) > 10. Determine the mean of the sampling distribution of p. HA = E (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of p. OA = (Round to six decimal places as needed.) (b) What is the probability of obtaining x = 23 or more individuals with the characteristic? That is, what is P(p20.46)? P(p20.46) = (Round to four decimal places as needed.) (c) What is the probability of obtaining x = 18 or fewer individuals with the characteristic? That is, what is P(ps0.36)? P(ps0.36) = (Round to four decimal places as needed.)
Suppose a simple random sample of size n = 50 is obtained from a population whose size is N = 10,000 and whose population proportion with a specified characteristic is p = 0.4. Complete parts (a) through (c) below. ..... (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. O A. Not normal because ns0.05N and np(1 - p)< 10. O B. Approximately normal because ns0.05N and np(1-p) < 10. OC. Not normal because ns0.05N and np(1-p) 2 10. O D. Approximately normal because ns0.05N and np(1 - p) > 10. Determine the mean of the sampling distribution of p. HA = E (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of p. OA = (Round to six decimal places as needed.) (b) What is the probability of obtaining x = 23 or more individuals with the characteristic? That is, what is P(p20.46)? P(p20.46) = (Round to four decimal places as needed.) (c) What is the probability of obtaining x = 18 or fewer individuals with the characteristic? That is, what is P(ps0.36)? P(ps0.36) = (Round to four decimal places as needed.)
MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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![Suppose a simple random sample of size n = 50 is obtained from a population whose size is N = 10,000 and whose population proportion with a specified characteristic is p = 0.4. Complete parts (a) through (c) below.
---
**(a) Describe the sampling distribution of \( \hat{p} \).**
Choose the phrase that best describes the shape of the sampling distribution below.
- **A.** Not normal because n ≤ 0.05N and np(1−p) < 10.
- **B.** Approximately normal because n ≤ 0.05N and np(1−p) < 10.
- **C.** Not normal because n ≤ 0.05N and np(1−p) ≥ 10.
- **D.** Approximately normal because n ≤ 0.05N and np(1−p) ≥ 10.
Determine the mean of the sampling distribution of \( \hat{p} \).
\[ \mu_{\hat{p}} = \, \_\_\_ \] (Round to one decimal place as needed.)
Determine the standard deviation of the sampling distribution of \( \hat{p} \).
\[ \sigma_{\hat{p}} = \, \_\_\_ \] (Round to six decimal places as needed.)
---
**(b) What is the probability of obtaining x = 23 or more individuals with the characteristic?** That is, what is \( P(\hat{p} ≥ 0.46) \)?
\[ P(\hat{p} ≥ 0.46) = \, \_\_\_ \] (Round to four decimal places as needed.)
---
**(c) What is the probability of obtaining x = 18 or fewer individuals with the characteristic?** That is, what is \( P(\hat{p} ≤ 0.36) \)?
\[ P(\hat{p} ≤ 0.36) = \, \_\_\_ \] (Round to four decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5498129d-fa90-4054-9767-1cffe54599e5%2F5bba43a0-9aa0-4d9c-ac4e-b653396a0c21%2Futzstq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose a simple random sample of size n = 50 is obtained from a population whose size is N = 10,000 and whose population proportion with a specified characteristic is p = 0.4. Complete parts (a) through (c) below.
---
**(a) Describe the sampling distribution of \( \hat{p} \).**
Choose the phrase that best describes the shape of the sampling distribution below.
- **A.** Not normal because n ≤ 0.05N and np(1−p) < 10.
- **B.** Approximately normal because n ≤ 0.05N and np(1−p) < 10.
- **C.** Not normal because n ≤ 0.05N and np(1−p) ≥ 10.
- **D.** Approximately normal because n ≤ 0.05N and np(1−p) ≥ 10.
Determine the mean of the sampling distribution of \( \hat{p} \).
\[ \mu_{\hat{p}} = \, \_\_\_ \] (Round to one decimal place as needed.)
Determine the standard deviation of the sampling distribution of \( \hat{p} \).
\[ \sigma_{\hat{p}} = \, \_\_\_ \] (Round to six decimal places as needed.)
---
**(b) What is the probability of obtaining x = 23 or more individuals with the characteristic?** That is, what is \( P(\hat{p} ≥ 0.46) \)?
\[ P(\hat{p} ≥ 0.46) = \, \_\_\_ \] (Round to four decimal places as needed.)
---
**(c) What is the probability of obtaining x = 18 or fewer individuals with the characteristic?** That is, what is \( P(\hat{p} ≤ 0.36) \)?
\[ P(\hat{p} ≤ 0.36) = \, \_\_\_ \] (Round to four decimal places as needed.)
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