Answer:
a) P(X > 10) = 0.6473
b) P(X > 20) = 0.4190
c) P(X < 30) = 0.7288
d) x = 68.87
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
In which is the decay parameter.
The probability that x is lower or equal to a is given by:
Which has the following solution:
The probability of finding a value higher than x is:
Mean equal to 23.
This means that
(a) P(X >10)
So
P(X > 10) = 0.6473
(b) P(X >20)
So
P(X > 20) = 0.4190
(c) P(X <30)
So
P(X < 30) = 0.7288
(d) Find the value of x such that P(X > x) = 0.05
So