Question

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 = 0.25. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. O A. Approximately normal, HA = 0.25 and 0.0004 p O B. Approximately normal, HA = 0.25 and 6 20.0137 'p OC. Approximately normal, Ha = 0.25 and on 0.0002 р р р (b) What is the probability of obtaining x = 280 or more individuals with the characteristic? P(x 2 280) = (Round to four decimal places as needed.) (c) What is the probability of obtaining x = 230 or fewer individuals with the characteristic? P(X s 230)=(Round to four decimal places as needed.)

Answer 1

n = 1ooo 2 p=0.25 N=1000000 @ în Normal (eep =p 1 PC1-P) ) Mp3 P=0.25 60 = 0.25(1-0,25) = = 0.000 1875 0.0137 0,1875 1000 1 000 B) Approximately Normal, ela = 0.25 and 6 o 7 0,0137 1 X N Normal (el=np 6=50pci-p) ) u=ne = 1000 (0.25) =210 620P(1-P) 1000 (0.25) (1-0,25) 118715 = 13.693 = 1 (6 © P(x3,280)=P[x= کی 30 XN Normal (ll= 250 =13.693) = 8 x - 4 > 280-250 13.693 =P[z z 13.693 = P(27 2.19) 31- P(Z = 2:19) E1 - 0.9982 PCX 7280) = 0.0018

P(x =230) < 230-250 = PX-ll 5 13.693 Plz -2o 13.693 - P(Z < -1.46) P(2 > 1.46) = 1 - P(Z <1:46) = 1- 0.9279 = 0,0721 IP(x=230)