Q:

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 . What is the probability of obtaining x = 520 or more individuals with the​ characteristic?

Accepted Solution

A:
Answer:[tex]p(x\geq 520)  = 0.0293[/tex]Step-by-step explanation:Given data: random sample size n = 1000Population size is N - 2,000,000P = 0.49We know [tex]\sigma_p = \sqrt{\frac{p*(1-p)}{n}}[/tex][tex]\sigma_ p = \sqrt{\frac{0.49*(1-0.49)}{1000}} = 0.0158[/tex]Probability for having X =520sample proportion [tex]\hat p = \frac{520}{1000} = 0.52[/tex][tex]p(x\geq 520)  = P(\hat p\geq) [/tex]                        [tex]= P(Z\geq \frac{0.52 - 0.49}{0.0158})[/tex]                        [tex]= P(Z\geq 1.89) = 0.0293[/tex][tex]p(x\geq 520)  = 0.0293[/tex]