Sampling distribution of p̂ is approximately normal if np
>=10 and n (1-p) >= 10
n * p = 150 * 0.2 = 30
n * (1 - p ) = 150 * (1 - 0.2) = 120
Mean = = p = 0.2
Standard deviation =
= 0.03266
X ~ N ( µ = 0.2 , σ = 0.03266 )
P ( X ≥ 0.26 ) = 1 - P ( X < 0.26 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 0.26 - 0.2 ) / 0.03266
Z = 1.8371
P ( ( X - µ ) / σ ) > ( 0.26 - 0.2 ) / 0.03266 )
P ( Z > 1.8371 )
P ( X ≥ 0.26 ) = 1 - P ( Z < 1.8371 )
P ( X ≥ 0.26 ) = 1 - 0.9669
P ( X ≥ 0.26 ) = 0.0331
X ~ N ( µ = 0.2 , σ = 0.03266 )
P ( X ≤ 0.18 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 0.18 - 0.2 ) / 0.03266
Z = -0.6124
P ( ( X - µ ) / σ ) < ( 0.18 - 0.2 ) / 0.03266 )
P ( X ≤ 0.18 ) = P ( Z < -0.6124 )
P ( X ≤ 0.18 ) = 0.2701
e Suppose a simple random sample of size n= 150 is obtained from a population whose...
e Question Help Suppose a simple random sample of size n=150 is obtained from a population whose size is N=25,000 and whose population proportion with a specified characteristic is p=0.2 Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). H = 0.2 (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)...
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 characteristicis p=02 bts Click here to view the standard normal distribution table (page 11 Click here to view the standard normal distribution table (page 2) HA=02 (Round to one decimal place as needed) Determine the standard deviation of the sampling distribution of GA 0.326599 (Round to six decimal places as needed) Pulm (b) What is...
Suppose a simple random sample of size n=1000 is obtained from a population whose size is N=1,000,000 and whose population proportion with a specified characteristic is p=0.56. Complete parts (a) through (c) below Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2) (a) Describe the sampling distribution of p O A. Approximately normal, A=0.56 and CAR 0.0005 OB. Approximately normal, Ha=0.56 and 0.0002 &c. Approximately normal, p=0.56...
Suppose a simple random sample of size n=200 is obtained from a population whose size is N = 30,000 and whose population proportion with a specified characteristic is p=0.4. Complete parts (a) through (c) below. Click Here for StatCrunch (a) Describe the sampling distribution of P. Determine the mean of the sampling distribution of . Hq (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of p. 0.- (Round to six decimal places as...
Suppose a simple random sample of size 150 is obtained from a population whose size is N 30,000 and whose population proportion with a specified characteristic is p0.8. (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 p(1-P) 10. OB. Approximately normal because ns0.05N and p1 - p) < 10. OC. Approximately normal because ns0.05N and no 1- 10 OD. Not normal...
Suppose a simple random sample of size n=200 is obtained from a population whose size is N= 30,000 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. A. Not normal because ns0.05N and np(1-P) 10. B. Not normal because ns 0.05N and np(1-p) < 10. C. Approximately normal because ns0.05N and...
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=0.49. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. O A. Approximately normal, ha = 0.49 and 04 0.0002 OB. Approximately normal, H = 0.49 and 04 <0.0004 C. Approximately normal, HA = 0.49 and 4 20.0158 (b) What is the probability of obtaining x=510 or more individuals...
Suppose a simple random sample of size n=200 is obtained from a population whose size is N = 30,000 and whose population proportion with a specified Charadelei isp.06. Complete purt (a) through k) below O C. Not normal because no.05N and np(1-P) 10 OD. Approximately normal because 0.05N and np{1 - p)<10 P Determine the mean of the sampling distribution of 06 (Round to one decimal place as noeded) Determine the standard deviation of the sampling distribution of 0.0.034541 (Round...
Suppose a simple random sample of size 150 is obtained from a population whose size is N15.000 and whose population proportion with a specified characteristic hp 04. Complete parts () through (c) below. (a) Describe the sampling distribution of Choose the phrase that best describes the shape of the sampling distribution below. O A. Approximately normal because 0.05 and 1-10 OB. Approximately normal becausen 00N and re-<10 OG Not normal because 0.06 and 1-12 10 OD. Not normalen SOON and...
Suppose a simple random sample of size n = 75 is obtained from a population whose size is N = 10,000 and whose population proportion with a specified characteristic is p=0.6. 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 n s 0.05N and np(1-p) < 10. O B. Not normal because ns0.05N and np(1-P) 2 10. O...