Let X= the weight of cocoa: X∼N(μ,σ2).
Given μ=650 kg,σ=35 kg.
i.
P(X<550)=P(Z<35550−650)
≈P(Z<−2.857143)≈0.002137
n=0.002137(350)=1
ii.
P(570<X<670)=P(X<670)−P(Z≤570)
=P(Z<35670−650)−P(Z≤35570−650)
≈P(Z<0.571429)−P(Z≤−2.2857149)
≈0.7161456−0.0111355≈0.705010
n=0.705010(350)=248
iii.
P(X>700)=1−P(Z≤700)
=1−P(Z≤35700−650)
≈1−P(Z≤1.428571)
≈0.076564
n=0.076564(350)=27
Comments
Leave a comment