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 (a) Describe the sampling distribution of p A. Approxmately normal, 0 46 and . ~ 0 0004 B. Approximately normal, ^-046 and . ~ 0 0002 O C. (b) What is the probability of obtaining x 490 or more individuals with the characteristic? PlX2490)-(Round to tour decmal places as needed) (c) What is the probability of obtaining x 440 or fewer individuals with the characteristic? P(X s440)(Round to four decimal places as needed) Approximately normal, 0 46 and o. ~ 0 01 58 Click to select your answerls). O Type here to search

Explanation / Answer

a) Option C) is correct

Mu (phat) = p = 0.46

sigma (phat) = sqrt(pq/n) = sqrt(0.46*0.54/1000) = 0.0158

b) Mean = np = 0.46*1000 = 460

St. deviation S = sqrt(npq) = sqrt(1000*0.46*0.54) =15.761

P(X>= 490)

Z1 = (490-460)/15.761 =1.90

P(X>=490) = P(Z>=1.90) =0.5-0.4713 =0.0287

c) P(X<=440)

Z1 = (440-460)/15.761 = -1.27

P(X<=440)= P(Z<=-1.27) =0.5-0.3980 =0.1020

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