Which of the following situations can be best modeled using a continuous distribution?

a) Number of heads in 10 flips of coin.
b) Number of customers/hr.
c) Time between arrivals of two customers.
d) Yes or no answer.
e) Number of product defects/hr.

Think of a continuous distribution having an infinite possibility of values, such as time, weight, and height. Look at each of your choices and see which best fits this.

Well, let me see if I can crack a joke to help you remember this one.

Why did the math book go to therapy?

Because it had too many issues!

Now, back to your question. The situation that can be best modeled using a continuous distribution would be c) Time between arrivals of two customers. This is because it involves a continuous variable (time) and can take on any value within a certain range. The other options involve discrete variables, so they would be better suited for a discrete distribution. But hey, don't worry, even if continuous distributions can be a bit tricky, with a little practice, you'll be modeling them like a pro!

The situation that can be best modeled using a continuous distribution is:

c) Time between arrivals of two customers.

Continuous distributions are used to model situations where the outcome can take on any value within a range or interval. In this case, the time between arrivals of two customers can take on any value, such as 2 minutes, 5 minutes, or 10 minutes, and it is not limited to specific discrete values. Therefore, a continuous distribution would be the most suitable model for this situation.

The situation that can be best modeled using a continuous distribution is c) Time between arrivals of two customers.

To understand why, let's go over the different options:

a) Number of heads in 10 flips of a coin: This situation involves a discrete distribution, as it only has a finite number of possible outcomes (0, 1, 2, 3, ..., 10).

b) Number of customers per hour: This situation can also be modeled using a discrete distribution, as the number of customers can only take on integer values (0, 1, 2, 3, ...).

c) Time between arrivals of two customers: This situation is best modeled using a continuous distribution, such as the exponential distribution. The time between customer arrivals can take on any non-negative real value (e.g., 0.5 minutes, 1.2 minutes, 2.3 minutes, etc.). Since time is continuous, a continuous distribution is appropriate for this situation.

d) Yes or no answer: This situation can be modeled using a discrete distribution, as there are only two possible outcomes (yes or no).

e) Number of product defects per hour: Similar to option b, this situation involves a discrete distribution since the number of defects can only take on integer values (0, 1, 2, 3, ...).

In summary, the situation that can be best modeled using a continuous distribution is c) Time between arrivals of two customers.