Using the exponential distribution, it is found that there is a 0.4462 = 44.62% probability that a customer waits less than 39 seconds.
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
In this problem, mean of 66 seconds, hence, the decay parameter is:
[tex]\mu = \frac{1}{66}[/tex]
The probability that a customer waits less than 39 seconds is:
[tex]P(X \leq 39) = 1 - e^{-\frac{39}{66}} = 0.4462[/tex]
0.4462 = 44.62% probability that a customer waits less than 39 seconds.
A similar problem is given at https://brainly.com/question/17039711
