Answer :
Answer:
[tex]p(x\geq 520) = 0.0293[/tex]
Step-by-step explanation:
Given data:
random sample size n = 1000
Population size is N - 2,000,000
P = 0.49
We 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 =520
sample 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]
Answer:
P(X≥520) =0.02938
Step-by-step explanation:
given,
n = 1000
Population size = N = 2,000,000
Specified characteristic = P = 0.49
Probability of obtaining x = 520
[tex]\sigma_p = \sqrt{\dfrac{p(1-p)}{1000}}[/tex]
[tex]\sigma_p = \sqrt{\dfrac{0.49(1-0.49)}{1000}}[/tex]
[tex]\sigma_p =0.0158[/tex]
for x = 520
p = 520/1000 = 0.52
P(X≥520) = P(p≥0.52)
P(p≥0.52) = [tex]P(Z\geq \dfrac{0.52-0.49}{0.0158})[/tex]
P(p≥0.52) = [tex]P(Z\geq 1.898)[/tex]
using z-table
P(p≥0.52) = 0.02938
P(X≥520) =0.02938