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STA 2171 HW3 Page 3 of 12 2. We know under certain conditions that the Normal distribution approximates the Bino- mial distri
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Answer #1

Suppose X ~ Poisson (60) where 09 =

(a) The mean of X is

A = A = 60

The variance of X is

= 1 = 60

(b) Use the normal approximation with the continuity correction, the probability is described as

P(58 < X < 62) = P(58 -0.5 <Y < 62 +0.5)

P(58 < X < 62) = P(57.5 <Y < 62.5)

Under central limit theorem,

P(57.5 <Y < 62,5) = P(57.5 - 60 P(57.5 Y 02.0) = Y - Hr62.5 - 60 0 60 60 -

P(57.5 <Y < 62.5) = P(-0.3227 < Z < 0.3227)

P(57.5 <Y < 62.5) = P(Z < 0.3227) - P(Z < -0.3227)

P(57.5 <Y < 62.5) = 0 (0.3227) - o(-0.3227)

Using standard normal table,

P(57.5 <Y < 62.5) = 0.6265 – 0.3734 = 0.2531

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