It is found that the time (in minutes) required by a predator to find a prey is

Question

It is found that the time (in minutes) required by a predator to find a prey is a random variable that is exponentially distributed with mu = 30. A. According to this distribution, what is the longest time within which the predator will be 80% certain of finding a prey? B. What is the probability that the predator will have to spend more than 1 hour looking for a prey? A. The longest time within which the predator will be 80% certain of finding a prey is minutes (Round to one decimal place as needed) B. The probability that the predator we have to spend more than 1 hour looking for a prey is (Round to four decimal places as needed)

Explanation / Answer

mean = 30 min

a = lambda = 1 / 30

f(x) = a*e^(-ax)

F(x) = 1 -e^(-ax)

a) longest time

P(X < t) = 0.80

1 - e^(-t/30) = 0.80

e^(-t/30) = 0.20

t = 48.2831 min

b) P(X> 1 hour) = P(X> 60) = 1- P(X < 60) = 1 -F(60) = 1- (1 -e^(- 1/30 *60))

= e^(-2)

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