SOLUTION FOR HOMEWORK 10, STAT 4351 Welcome to your 10th ...
SOLUTION FOR HOMEWORK 10, STAT 4351 Welcome to your 10th ...
SOLUTION FOR HOMEWORK 10, STAT 4351 Welcome to your 10th ...
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<strong>10</strong>. Problem 6.78. Here we study X b ∼ Bin(p = .23, n = 120). Then µ = np = 27.6,<br />
σ = [np(1 − p)] 1/2 = [(27.6)(.77)] 1/2 = 4.61. Using Normal approximation<br />
P(X b > 32) = P(X N > 32.5) = P( X N − µ<br />
σ<br />
> 32.5 − µ )<br />
σ<br />
= P(Z > 32.5 − µ ) = P(Z > 1.06).<br />
σ<br />
Here Z is the standard normal random variable. Then I use Normal Table in the Text and<br />
get<br />
P(Z > 1.06) = .5000 − P(0 ≤ Z ≤ 1.06) = .5000 − .3554 = .1446.<br />
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