Question: "What do you think is the ideal number of children for a family to have?" A Gallup Poll asked this question of 300 randomly chosen adults. Almost half $(49 \%)$ thought two children was ideal. Suppose that $p=0.49$ is exactly true for the population of all adults. Gallup announced a margin of error of $\pm 3$ percentage points for this poll. What is the probability that the sample proportion $\hat{p}$ falls between 0.46 and 0.52? What is the probability that the sample proportion $\hat{p}$ falls between 0.46 and 0.52 if $n=5000$ ?

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