Question

# "What do you think is the ideal number of children for a family to have?" A...

"What do you think is the ideal number of children for a family to have?" A Gallup Poll asked this question of 1016 randomly chosen adults. Almost half (49%) thought two children was ideal.† We are supposing that the proportion of all adults who think that two children is ideal is p = 0.49.
What is the probability that a sample proportion falls between 0.46 and 0.52 (that is, within ±3 percentage points of the true p) if the sample is an SRS of size n = 200?(Round your answer to four decimal places.)

What is the probability that a sample proportion falls between 0.46 and 0.52 if the sample is an SRS of size n = 5000? (Round your answer to four decimal places.)

1)

 for normal distribution z score =(p̂-p)/σp here population proportion=     p= 0.490 sample size       =n= 200 std error of proportion=σp=√(p*(1-p)/n)= 0.0353
 probability = P(0.46

2)

 sample size       =n= 5000 std error of proportion=σp=√(p*(1-p)/n)= 0.0071
 probability = P(0.46

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