Suppose that $x$ has a binomial distribution with $n = 200$ and $p = .5$. (a) Show that the normal approximation to the binomial can appropriately be used to calculate probabilities about $x$ Both $np$ and $n(1 - p)$ exceed 10 (b) Make continuity corrections for each of the following, and then use the normal approximation to the binomial to find the following probabilities: (Round your $z$ answers to 2 decimal places. Round your $\sigma$ and $P$ values to 4 decimal places.) $\mu = $ $\sigma = $ 1. $P(x = 80)$ 2. $P(x \le 95)$ 3. $P(x < 65)$ 4. $P(x \ge 100)$ 5. $P(x > 100)$
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5$. We need to check if both $np$ and $n(1-p)$ exceed 10. $np = 200 \times 0.5 = 100$ $n(1-p) = 200 \times (1 - 0.5) = 100$ Since both $np$ and $n(1-p)$ are greater than 10, the normal approximation to the binomial can be used. Show more…
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