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P(a ≤ X ≤ b) ‡ P(a0.5 ≤ Y ≤ b+0.5)
where Y has a normal distribution with the same mean and standard deviation as X; that is,
µ = np and ß = np(1p) . Notes
1. The condition that 0 ≤ µ3ß < µ+3ß ≤ n is satisfied if n is sufficiently large and p is
not too close to 0 or 1, and ensures that almost all of the normal curve lies in the range 0
to n.
2. In the formula P(a ≤ X ≤ b) ‡ P(a0.5 ≤ Y ≤ b+0.5) we assume that a and b are
integers. The use of a0.5 and b+0.5 is called the continuity correction. To see that it
is necessary, consider what...
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 Spring '13
 Herbret
 Statistics, Normal Distribution, Standard Deviation, Probability theory, Binomial distribution

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