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atroni [7]
2 years ago
12

Suppose a simple random sample of size n = 1000 is obtained from a population whose size is N = 2,000,000 and whose population p

roportion with a specified characteristic is p = 0.49 . What is the probability of obtaining x = 520 or more individuals with the​ characteristic?
Mathematics
2 answers:
faltersainse [42]2 years ago
6 0

Answer:

p(x\geq 520)  = 0.0293

Step-by-step explanation:

Given data:

random sample size n = 1000

Population size is N - 2,000,000

P = 0.49

We know

\sigma_p = \sqrt{\frac{p*(1-p)}{n}}

\sigma_ p = \sqrt{\frac{0.49*(1-0.49)}{1000}} = 0.0158

Probability for having X =520

sample proportion \hat p = \frac{520}{1000} = 0.52

p(x\geq 520)  = P(\hat p\geq)

                       = P(Z\geq \frac{0.52 - 0.49}{0.0158})

                       = P(Z\geq 1.89) = 0.0293

p(x\geq 520)  = 0.0293

Amanda [17]2 years ago
5 0

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

\sigma_p = \sqrt{\dfrac{p(1-p)}{1000}}

\sigma_p = \sqrt{\dfrac{0.49(1-0.49)}{1000}}

\sigma_p =0.0158

for x = 520

p = 520/1000 = 0.52

P(X≥520) = P(p≥0.52)

P(p≥0.52) = P(Z\geq \dfrac{0.52-0.49}{0.0158})

P(p≥0.52) = P(Z\geq 1.898)

using z-table

P(p≥0.52) = 0.02938

P(X≥520) =0.02938

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