Question

Suppose a simple random sample of size n = 200 is obtained from a population whose size is N = 10,000 and whose population proportion with a specified characteristic is p = 0.8. (a) Describe the sampling distribution of 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 p?. ?_p? = (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of p?. ?_p? = (Round to six decimal places as needed.) (b) What is the probability of obtaining x = 164 or more individuals with the characteristic? That is, what is P(p? ? 0.82)? P(p? ? 0.82) = (Round to four decimal places as needed.) (c) What is the probability of obtaining x = 150 or fewer individuals with the characteristic? That is, what is P(p? ? 0.75)? P(p? ? 0.75) = (Round to four decimal places as needed.)

          Suppose a simple random sample of size n = 200 is obtained from a population whose size is N = 10,000 and whose population proportion with a specified characteristic is p = 0.8.

(a) Describe the sampling distribution of 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 p?.
?_p? = (Round to one decimal place as needed.)

Determine the standard deviation of the sampling distribution of p?.
?_p? = (Round to six decimal places as needed.)

(b) What is the probability of obtaining x = 164 or more individuals with the characteristic? That is, what is P(p? ? 0.82)?
P(p? ? 0.82) = (Round to four decimal places as needed.)

(c) What is the probability of obtaining x = 150 or fewer individuals with the characteristic? That is, what is P(p? ? 0.75)?
P(p? ? 0.75) = (Round to four decimal places as needed.)

Suppose a simple random sample of size n = 200 is obtained from a population whose size is N = 10,000 and whose population proportion with a specified characteristic is p = 0.8.

(a) Describe the sampling distribution of 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 p?.
?p? = (Round to one decimal place as needed.)

Determine the standard deviation of the sampling distribution of p?.
?p? = (Round to six decimal places as needed.)

(b) What is the probability of obtaining x = 164 or more individuals with the characteristic? That is, what is P(p? ? 0.82)?
P(p? ? 0.82) = (Round to four decimal places as needed.)

(c) What is the probability of obtaining x = 150 or fewer individuals with the characteristic? That is, what is P(p? ? 0.75)?
P(p? ? 0.75) = (Round to four decimal places as needed.)

Added by Adam G.

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