Suppose a simple random sample of size n-1000 is obtained from a population whos

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 Complete parts (a) through (c) below s p 056 (a) Describe the sampling distribution of p. O A. Approximately normal.: 0 56 and ^ .0004 B. Approximately normal, .: 056 ando. 00157 A: Approximately normal. :056 and ap ~00002 (b) What is the probability of obtaining x 590 or more individuals with the characteristic? POx a 590-0.02 (Round to four decrnal places as needed ) (c) What is the probability of obtaining x- 520 or fewer individuals with the characteristic? Pox s 520)- Round to four decimal places as needed) Enter your answer in the answer box and then click Check Answer Clear Al ype here to search DOLL

Explanation / Answer

Sampling distribution of p is distribution that would results if one repeatedly samples n=1000 from a speciifed population and note the proportion, p with specified characteristic. The mean is 0.56 and standard devaition is sqrt[phat(1-phat)/n]=sqrt[0.56(1-0.56)/1000]=0.0157

P(X>=590)=P(phat>=0.59)=P[Z>=(0.59-0.56)/0.0157]=P(Z>=1.91)

In order to find area beyond a positive Z score, look into z table and find area corresponding to the Z score and then subtract the area from 1, because the Z table gives area under standard normal curve to the left of Z. The required probability is: 1-0.9719=0.0281

P(X<=520)=P(phat<=0.52)=P(Z<=(0.52-0.56)/0.0157]=P(Z<=-2.55)=0.0054

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