我有一個大學的機率數學題 ><!急
a police department needs new tires for its patrol cars and the probabilities are 0.15,0.24,0.03,0.28,0.22,and 0.08 that it will buy uniroyal tires, goodyear tires, michelin tires, general tires,goodrich tires,or armstrong tires. find the probabilities that will buy:
a. goodyear or goodrich tires;
b. uniroyal,michelin, or goodrich gires;
c.michelin or armstrong tires;
d uniroyal, michelin, general, or goodrich tires
please step by step
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A police department needs new tires for its patrol cars and the probabilities are uniroyal tires, 0.15goodyear tires, 0.24michelin tires, 0.03general tires, 0.28goodrich tires, 0.22armstrong tires, 0.08 Sum=1μ=average=1/6=0.16666667S=√[V/(n-1)]=stdev=0.097502σ=0.097502/√5Please step by step find the probabilities for buying(a) goodyear or goodrich tiresX=0.24+0.22=0.46Z=(0.46-0.16667)/(0.097502/√5)=6.7P(0<=Z<=6.7)=100%
(b) uniroyal, michelin, or goodrich gires;X=0.15+0.03+0.22=0.4Z=(0.4-0.166667)/(0.097502/√5)=5.35P(0<=Z<=5.35)=100%
c.michelin or armstrong tires;X=0.03+0.08=0.11Z=(0.11-0.166667)/(0.097502/√5)=-1.3P(Z<=-1.3)=0.5-P(0.5<=Z<=1.3)=0.5-0.4032=0.0968=9.68%
d uniroyal, michelin, general, or goodrich tiresX=0.15+0.03+0.28+0.22=0.68Z=(0.68-0.16667)/(0.097502/√5)=11.8P(0<=Z<=11.8)=100%