Answer to Question #245802 in Statistics and Probability for APII

Question

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. 

Answer 1

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

(a)

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

(b)

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

(c)

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