Let X= the life length of a certain brand A of an electronic device: X∼N(μ1,σ12).
Let Y= the life length of a certain brand B of an electronic device: Y∼N(μ2,σ22).
Given
μ1=40 h,σ1=3 h,
μ2=45 h,σ2=6 h
(a)
P(X≥45)=1−P(X<45)
=1−P(Z<345−40)≈1−P(Z<1.6667)
≈0.0478
P(Y≥45)=1−P(Y<45)
=1−P(Z<645−45)=1−P(Z<0)
=0.5Brands B should be preferred for a continuous use of 45 hours.
(b)
P(X≥55)=1−P(X<55)
=1−P(Z<355−40)≈1−P(Z<5)
≈0.0000003
P(Y≥55)=1−P(Y<55)
=1−P(Z<655−45)=1−P(Z<1.6667)
≈0.0478Brands B should be preferred for a continuous use of 55 hours.
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