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?
You are interested in the probabiliity of the bomb falling within 40 feet of its target. I am not sure where you got the number 100 from.I am wondering why I have not used the interval 0<x<100.
for part (b) you can use the binomial distribution. You will have to assume that the outcome of each bomb drop is independant.
For large bombs:
You have 3 trials, and you worked out the probability of success on each trial in part (a)
For small bombs:
You have eight trials, and you need to work out the probability of success on each trial. Use the same method as part (a)