A trucker hauls material between town A and Town B suppose t

A trucker hauls material between town A and Town B. suppose the round-trip duration X(in hours) is an Exponential RV with lambda=0.05

1.Find P(X<=40 | X>15)

2.Assume round-trip durations are independent from one trip to the next. Find the probability that exactly two of the next five round trips take more than 25 hours.

Solution

1.

p(X<=40|X>15) = P(15<x<40) / P(x>15)

= (exp(-0.05*15) - exp(-0.05*40))/(exp(-0.05*15)

= 0.713495203 [ANSWER]

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2.

Note that

P(more than 25) = exp(-0.05*25) = 0.286504797

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    5      
p = the probability of a success =    0.286504797      
x = the number of successes =    2      
          
Thus, the probability is          
          
P (    2   ) =    0.298151479 [ANSWER]