) During a professor’s oce hours, students arrive, on average, every ten minutes. Assume that the distribution of the time between arrivals follows an exponential distribution. Suppose that a student has just le. What is the probability that the professor has more than 25 minutes before the next student shows up?

8.21% probability that the professor has more than 25 minutes before the next student shows up

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:

During a professor’s oce hours, students arrive, on average, every ten minutes.

This means that

What is the probability that the professor has more than 25 minutes before the next student shows up?

Either he has 25 minutes or less, or he has more than 25 minutes. The sum of the probabilities of these events is decimal 1. So

We want P(X > 25). So

In which

8.21% probability that the professor has more than 25 minutes before the next student shows up

location: point 0

step-by-step explanation:

well, -8 to 10 on a number line is 18 spaces.

1/9 of 18 is 2.

so, 4/9 of 18 must be 8.

8 spaces from -8 (a) is 0.

so, 4/9 of the way from -8 to 10 is 0!