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--- b:head_first_statistics:using_the_normal_distribution [2025/10/08 12:06] – [Independent Observation] hkimscil
+++ b:head_first_statistics:using_the_normal_distribution [2025/10/08 12:11] (current) – [Pool Puzzle] hkimscil
@@ Line 633: / Line 633: @@
 Before going further:
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 So what’s the probability of getting 30 or more questions right out of 40? That will help us determine whether to keep playing, or walk away.
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 There are 40 questions, which means there are 40 trials.
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 <code>
 > pbinom(29,40, 1/4, lower.tail = F)
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 {{:b:head_first_statistics:pasted:20191118-095652.png}}
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 이를 R을 이용하여 구하면,
 <code>
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 이 값은 위의 0.387에 근사하다.
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   * In particular circumstances you can **use the normal distribution to approximate the binomial**. If X ~ B(n, p) and np > 5 and nq > 5 then you can approximate X using X ~ N(np, npq)
   * If you’re approximating the binomial distribution with the normal distribution, then you need to **<fc #ff0000>apply a continuity correction</fc>** to make sure your results are accurate.
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 {{:b:head_first_statistics:pasted:20191118-103328.png}}
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 Q:Does it really save time to approximate the binomial distribution with the normal?
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 ===== Pool Puzzle =====
 <wrap #continuity_correction_egs />
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 X < 3  ----  <wrap spoiler> X < 2.5 </wrap>
 X > 3  ----  <wrap spoiler> X > 3.5 </wrap>