Unformatted text preview: Z <
⎜
Then 12 −12.1
σ / 100 ⎝
= 2.58 and σ = 0.388 . 12 − 12.1 ⎞
⎟ = 0.005.
⎟
σ / 100 ⎠ ⎛ 12 − 12.1 ⎞
⎟ = 0.01.
⎟
0.5 / n ⎠
⎝
= 2.33 and n = 135.72 ≅ 136 . e) P( X < 12) = 0.01 implies that P⎜ Z <
⎜
Then
563 12 −12.1
0.5 / n Let X denote the average thickness of 10 wafers. Then, E( X ) = 10 and V( X ) = 0.1.
a) P (9 < X < 11) = P ( 9 −10 < Z < 11−10 ) = P(−3.16 < Z < 3.16) = 0.998 .
0.1
0.1
The answer is 1 − 0.998 = 0.002
b) P ( X > 11) = 0.01 and σ X =
Therefore, P( X > 11) = P( Z > 1
n 11−10
1
n . ) = 0.01 , 11 − 10
1 = 2.33 and n = 5.43 which is n rounded up to 6.
c) P ( X > 11) = 0.0005 and σ X = σ
Therefore, P( X > 11) = P( Z > 11−10 σ 10 . ) = 0.0005 , 10 11−10 σ = 3.29 10 σ = 10 /...
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This document was uploaded on 02/09/2014.
 Spring '14

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