Let X= the daily time to complete the task: X∼N(μ,σ2).
Then Z=σX−μ∼N(0,1)
Given μ=10 hours,σ=2 hours,N=800
i.
P(X<8)=P(Z<28−10)=P(Z<−1)≈≈0.158655 n=0.158655×800=125
ii.
P(X<12.5)=P(Z<212.5−10)=P(Z<1.25)≈≈0.894350 n=0.894350×800=715
iii.
P(X>13.5)=1−P(X≤13.5)=
=1−P(Z≤213.5−10)=P(Z≤1.75)≈
≈1−0.959941=0.040059
n=0.040059×800=32
iv.
P(7.5<X<14)=P(X<14)−P(X≤7.5)=
=P(Z<214−10)−P(Z≤27.5−10)=
=P(Z<2)−P(Z≤−1.25)≈
≈0.977250−0.105650=0.8716
n=0.8716×800=697
v.
P(6.2<X<10)=P(X<10)−P(X≤6.2)=
=P(Z<210−10)−P(Z≤26.2−10)=
=P(Z<0)−P(Z≤−1.9)≈
≈0.5−0.028717=0.471283
n=0.471283×800=377
vi. Within 2 hours
P(10−2<X<10+2)=P(X<12)−P(X≤8)=
=P(Z<212−10)−P(Z≤28−10)=
=P(Z<1)−P(Z≤−1)≈
≈1−2(0.158655)=0.682690n=800−0.682690×800=254
The firm will lay-off 254 workers.
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