Let X= the amount of coffee in a cup: X∼N(μ,σ2).
Given μ=210 ml,σ=13.5 ml.
a)
P(X>231)=1−P(Z≤13.5231−210)
=1−P(Z≤914)≈0.0599 6% of the cups will contain more than 231 ml.
b)
P(180<X<220)=P(X<220)−P(X≤180)
=P(Z<13.5220−210)−P(Z≤13.5180−210)
≈0.7705747−0.0131341≈0.757441 0.757441
c)
P(X>235)=1−P(Z≤13.5235−210)
=1−P(Z≤2750)≈0.032024
0.032024(900)=29 29 cups
d)
P(X>x)=0.15P(X>x)=1−P(Z≤13.5x−210)=0.15
P(Z≤13.5x−210)=0.85
13.5x−210≈1.036433
x=224 224 ml.
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