The time between calls made to Amazon's customer service is exponentially distributed with a mean of 10 minutes (taken between each two successive calls). The probability that the time between the next two calls is between 3 minutes and 7 minutes is:

A. 0.7558
B. 0.5034
C. 0.2442
D. 0.2592

The probability that the time between the next two calls is between 3 minutes and 7 minutes is 0.2442.

Step-by-step explanation:

Let X = time between calls made to Amazon's customer service.

The average time between calls is, β = 10 minutes.

The random variable X follows an Exponential distribution with parameter

The probability distribution function of X is:

Compute the probability that the time between the next two calls is between 3 minutes and 7 minutes as follows:

Thus, the probability that the time between the next two calls is between 3 minutes and 7 minutes is 0.2442.

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.