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=0.49. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. O A. Approximately normal, ha = 0.49 and 04 0.0002 OB. Approximately normal, H = 0.49 and 04 <0.0004 C. Approximately normal, HA = 0.49 and 4 20.0158 (b) What is the probability of obtaining x=510 or more individuals with the characteristic? P(X2510)=L(Round to four decimal places as needed.) (c) What is the probability of obtaining x = 450 or fewer individuals with the characteristic? P(XS450)= (Round to four decimal places as needed.) Click to select your answer(s).

Answer 1

Given that, n = 1000 and proportion (p) = 0.49

a) The sampling distribution of $\hat p$ is approximately normal with mean and standard deviation are,

Mp=p=0.49

Op = p*(1 - p) 9 0.49 * (1 -0.49) 2 = 0.0158 1000 V

b) x = 510

sample proportion $(\hat p)$ = 510/1000 = 0.51

P(X > 510) = P(p>0.51) = P(Z > 0.51 -0.49 ) = P(Z > 1.27) = 0.1020 0.0158 1

=> P(X > 510) = 0.1020

c) x = 450

sample proportion $(\hat p)$ = 450/1000 = 0.45

P(X < 450) = P < 0.51) = P(Z < 0.4 9) = P(Z < -2.53) = 0.0057

=> P(X < 450) = 0.0057