Let X= mass of the soap: X∼N(μ,σ2).
Given μ=300 g,σ=52 g.
a)
P(X>320)=1−P(Z≤52320−300)
≈1−P(Z≤2.7735)≈0.002773
b)
P(280<X<500)=P(Z<52500−300)
−P(Z≤52280−300)≈P(Z≤27.7350)
−P(Z≤−2.7735)≈1−0.002773
≈0.997227
0.997227(100)=100 100 soaps will have masses between 280g and 500g.
Comments
Leave a comment