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. Describe the sampling distribution of p. Approximately normal, mu = 0 44 and sigma 0 0157 Approximately normal, mu = 0.44 and sigma 0.0004 Approximately normal, mu = 0.44 and sigma 0.0002 What is the probability of obtaining x = 460 or more individuals with the characteristic? P (x greaterthanorequalto 460) = (Round to four decimal places as needed) What is the probability of obtaining x = 410 or fewer individuals with the characteristic? P (x lessthanorequalto 410) = (Round to four decimal places as needed.)

Explanation / Answer

a) mean =0.44

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

hence option A is correct

b)here mean =np=1000*0.44=440

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

hence P(X>=460) =1-P(X<=459) =1-P(Z<(459.5-440)/15.697)=1-P(Z<1.2423)=1-0.8929=0.1071

c)P(X<=410)= P(Z<(410.5-440)/15.697)=P(Z<-1.8793)=0.0301

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.