Suppose a simple random sample of size n =150 is obtained from a population whose size is N =15,000 and whose population proportion with a specified characteristic is p=0.8. 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. A. Not normal because n<0.5N and np(1-p)<10. B. Approximately normal because n<0.5N and np(1-p)<10 C. Not normal because n<0.5N and np(1-p)>10 D. Approximately normal because n<0.5N and np(1-p)>10 Determine the mean of the sampling distribution of p. HA= (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of p. = (Round to six decimal places as needed) ​(b) What is the probability of obtaining x=123 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 =111 or fewer individuals with the​ characteristic? That​ is, what is ​P(p<0.74)? ​ P(p<0.74)? = ​(Round to four decimal places as​ needed.)

MATLAB: An Introduction with Applications
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Suppose a simple random sample of size n =150 is obtained from a population whose size is N =15,000 and whose population proportion with a specified characteristic is p=0.8. 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.                                               A. Not normal because n<0.5N and np(1-p)<10.
B. Approximately normal because n<0.5N and np(1-p)<10
C. Not normal because n<0.5N and np(1-p)>10
D. Approximately normal because n<0.5N and np(1-p)>10
 
Determine the mean of the sampling distribution of p. HA=
 (Round to one decimal place as needed.)
 
Determine the standard deviation of the sampling distribution of p. =
 
(Round to six decimal places as needed)
 
​(b) What is the probability of obtaining
x=123
 
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 =111  or fewer individuals with the​ characteristic? That​ is, what is ​P(p<0.74)?  ​
P(p<0.74)? =
​(Round to four decimal places as​ needed.)
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