Question

"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 p̂ 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 = 400? (Round your answer to four decimal places.)

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

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all the answers in chegg is not correct please do your best

Answer 1

Given:

p= 0.49

(a) Here n=300, we will use z-test for proportions to calculate the probability,it would be as followed:

(b)When n=500, then the probability would be as followed: