statistics notes 4

5 y b05 where y has a normal distribution with the

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Unformatted text preview: hen P(a ≤ X ≤ b) ‡ P(a-0.5 ≤ 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(1-p) . Notes 1. The condition that 0 ≤ µ-3ß < 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(a-0.5 ≤ Y ≤ b+0.5) we assume that a and b are integers. The use of a-0.5 and b+0.5 is called the continuity correction. To see that it is necessary, consider what...
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