Suppose a simple random sample of size n = 1000 is obtained from a population wh

Question

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 = 0.44. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p^Hat. A. Approximately normal, mu _p^Hat = 0.44 and sigma _ p^Hat almostequalto 0.0002 B. Approximately normal, mu _p^Hat = 0.44 and sigma _ p^Hat almostequalto 0.0157 C. Approximately normal, mu _p^Hat = 0.44 and sigma _P^Hat almostequalto 0.0004 (b) What is the probability of obtaining x = 470 or more individuals with the characteristic? P(x greaterthanorequalto 470)= ___ (Round to four decimal places as needed.) (c) What is the probability of obtaining x = 420 or fewer individuals with the characteristic? P(x greaterthanorequalto 420) = ___ (Round to four decimal places as needed.)

Explanation / Answer

a)here mean proportion =p=0.44

and std error =(p(1-p)/n)1/2 =0.0157

therefore option B is right

b) mean number =np=0.44*100=440

and std deviation =(np(1-p))1/2 =15.697

therfore P(X>=470)=P(Z>(469.5-440)/15.697)=P(Z>1.8793)=0.0301

c)P(X<=420)=P(Z<(420.5-440)/15.697)=P(Z<-1.2423)=0.1071

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