Through the career services office, you have arranged preliminary interviews at four companies for summer jobs. Each company will either ask you to come to their site for a follow-up interview or not. Let X be the random variable equal to the total number of follow-up interviews that you might have. a) List all the possible values of X. b) Is the random variable discrete or continuous? c) Do you think a uniform distribution might be appropriate as a model for this random variable? Explain briefly.

a) All the possible values of X are: 0,1,2,3,4

b) Discrete

c) No.

For each job, there are only two possible outcomes. Either you asked for a follow up interview or not. This means that the most appropriate model is the binomial probability distribution.

Step-by-step explanation:

You have four interviews. Each one has two possible outcomes. Either you are asked to come back for a follow up interview or you are not.

Let X be the random variable equal to the total number of follow-up interviews that you might have.

a) List all the possible values of X.

This is the number of follow-up interviews you can be called.

You can be called to 0,1,2,3 or 4 follow up interviews.

So all the possible values of X are: 0,1,2,3,4.

b) Is the random variable discrete or continuous?

There are no decimal values. For example, you cannot be asked to 3.5 interviews, for example.

So the random variable is discrete.

c) Do you think a uniform distribution might be appropriate as a model for this random variable? Explain briefly.

No.

For each job, there are only two possible outcomes. Either you asked for a follow up interview or not. This means that the most appropriate model is the binomial probability distribution.