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 p0.52 Complete parts (a) through (c) below (a) Describe the sampling distribution of O A. Approximately normal. 052 and 0.0002 OB. Approximately normal, A = 0.52 and 0.0004 P P O C. Approximately normal, Ha=0.52 and C 0.0158 D (b) What is the probability of obtaining x 540 or more individuals with the characteristic? Plx 2540) - (Round to four decimal places as needed.) (c) What is the probability of obtaining x = 490 or fewer individuals with the characteristic? Pixs 490)=(Round to four decimal places as needed) Click to select your answers)

help please

Answer 1

suppose simple random sample of size no 1000 from whose size population obtained is N=2,000,000 ¢ whose population proportion with a specified characteristic is p= 0.52 complete (a) through cc distribution of 9) The sampling so * HA=P 0.52 4

rý c p* (1-P) 0.52*0.48 1000 0.0158 - n. correct option is ☺ Approximately Normal Mņ= 0.52 f on 211 0.0158 more b Probability of obtaining a=540 or individuals with the characteristic.

p Ca>,540) we con use Normal Approximahon : 520 4 4 Elx) = 12 БР 16oo to.52= v (X) = n pq = 1000+ 0.52*0.48 249.6 !. rcx) = Juixi 249.6 = 15.7987 Now, o e know that (-4) 2- ų Noll) 0

s 701:01 = &68-0-1 (6592.1>2)d- 2 deos 21904 asn mon [65921 izld (toets 58b:51 ozs-ons czo- 9 [mons Z Hz Jo = (onsito Jol

Probability of obtaining 2=490 or fewer individuals with the characteristic . = P(Z < 490) use approximahon Normal (n-x) 2= ( اره ) لم هه f r= 15.7987. here Ha 520 ܝ ܙ PCR < 490-520 is. 1987) لا

=P(2¢ -1.8989) (Now use 2 score table) = 1- Plz< 1.8989) = 10.0287 - 1- 0.9713