Question

Waiting times to receive food after placing an order at the local Subway sandwich shop follow an exponential distribution with a mean of 66 seconds. Calculate the probability a customer waits:a. Less than 39 seconds.

Answer 1

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:  

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

In this problem, mean of 66 seconds, hence, the decay parameter is:

$\mu = \frac{1}{66}$

The probability that a customer waits less than 39 seconds is:

$P(X \leq 39) = 1 - e^{-\frac{39}{66}} = 0.4462$

0.4462 = 44.62% probability that a customer waits less than 39 seconds.

A similar problem is given at brainly.com/question/17039711