a)
µ = 9
σ = 0.1
we need to calculate probability for ,
P ( 8.85 < X <
9.15 )
=P( (8.85-9)/0.1 < (X-µ)/σ < (9.15-9)/0.1 )
P ( -1.500 < Z <
1.500 )
= P ( Z < 1.500 ) - P ( Z
< -1.500 ) =
0.9332 - 0.0668 =
0.8664
required probability = 1 - 0.8664=0.1336
excel formula for probability from z score is
=NORMSDIST(Z)
defects found = 0.1336*1000 ≈134
b)
µ = 9
σ = 0.05
we need to calculate probability for ,
P ( 8.85 < X <
9.15 )
=P( (8.85-9)/0.05 < (X-µ)/σ < (9.15-9)/0.05 )
P ( -3.000 < Z <
3.000 )
= P ( Z < 3.000 ) - P ( Z
< -3.000 ) =
0.9987 - 0.0013 =
0.9973
required probability = 1 - 0.9973
=0.0027
defects found ≈3
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