Answer to Question #245802 in Statistics and Probability for APII

Question #245802

The probabilities that a furnace station will supply melted products to 0,1,2,3,4, 5 or more temperature controlled trucks during a certain 30-minute period are 0.03, 0.18, 0.24, 0.28, 0.10 and 0.17. Find the probability that in this 30-minute period (a) more than two trucks received melted products (b) at most 4 trucks received melted products and (c) 4 or more trucks received melted products. 


1
Expert's answer
2021-10-05T11:24:17-0400

P(X=0)=0.03P(X=1)=0.18P(X=2)=0.24P(X=3)=0.28P(X=4)=0.10P(X5)=0.17P(X=0) = 0.03 \\ P(X=1) = 0.18 \\ P(X=2) = 0.24 \\ P(X=3) = 0.28 \\ P(X=4) = 0.10 \\ P(X≥5) = 0.17

(a)

P(X>2)=1P(X2)=1[P(X=0)+P(X=1)+P(X=2)]=1[0.03+0.18+0.24]=10.45=0.55P(X>2) = 1 -P(X≤2) \\ = 1 -[P(X=0) + P(X=1) + P(X=2)] \\ = 1 -[0.03+0.18+0.24] \\ = 1 -0.45 \\ = 0.55

(b)

P(X4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)=0.03+0.18+0.24+0.28+0.1=0.83P(X≤4) = P(X=0) +P(X=1) + P(X=2) + P(X=3) + P(X=4) \\ = 0.03 + 0.18 + 0.24 +0.28 +0.1 \\ = 0.83

(c)

P(X4)=P(X=4)+P(X=5)=0.10+0.17=0.27P(X≥4) = P(X=4) +P(X=5) \\ = 0.10 + 0.17 \\ = 0.27


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