A bombing plane flies directly above a railroad track. Assume that if a large (small) bomb falls within 40 (15) feet of the track, the track will be sufficiently damaged so that the traffic will be disrupted. Let X denote the perpendicular distance from the track that a bomb falls. Assume that
[IMG]file:///C:/Users/Standard/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif[/IMG] fx(x) = (100 - x)/5000 I(0, 100) (x)
There are two problems. I would like somebody to check my work for this first problem.
(a) Find the probability that a large bomb will disrupt traffic.
I found the cdf of X by integrating the f(t) dt from -infinity to x
Actually from 0 to x integration of (100-t)/5000. Then I got the cdf as F(x) = 1/5000 [100x - (x^2/2)]
I used the cdf to find the probability between 0 and 40.
P(0 < x< 40) = P(x<40) - P(x<0) = F(40) - F(0)
Finally, I got the answer as 0.64
I am wondering why I have not used the interval 0<x<100.
I don't have an idea on how to solve the second problem that follows.
(b) If the plane can carry three large (eight small) bombs and uses all three (eight), what is the probability that the traffic will be disrupted?