Data Distributions

Details:

The purpose of this assignment is to apply data distributions to
discrete and continuous data and justify the selection of the distributions.

For this assignment, you will use the “Random Variables”
dataset. You will use SPSS to analyze the dataset and address the
questions presented. Findings should be presented in a Word document
along with the SPSS outputs.

Part 1:

Identify if the following random variables are discrete or continuous.

1. Number of defected items in a shipment.
2. Height of
   males (in mm) who attend Grand Canyon University.
3. Yearly
   income among all people in the United States.
4. Whether or
   not a high school graduate is accepted into a college.
5. Time
   that it takes for a person to run a mile.
6. The number of
   emergency hospital visits that each person had in the last 12
   months.

Part 2:

Let X be a random variable of the outcome after
rolling a six-sided die one time that is not fair. In fact,
the die is designed to never result in a 1 or 6, while the other
outcomes (i.e., 2, 3, 4, and 5) are equally probable.

1. What are the individual probabilities for all possible values
   of X?
2. What are the cumulative probabilities for
   all possible values of X?
3. What is = ?
4. What is = ?
5. What is = ?

Part 3:

The dataset provided consists of the following random variables:

1. BMI: The body mass index of a random set of
   people.
2. Distance: The distance (in feet) that a baseball
   player hit the ball.
3. Height: The height of males (in mm).
4. Income: The income (in dollars) of people in a
   large company.
5. Pass: The outcome when taking an exam (1=Pass;
   0=Fail).
6. Wait Time: The time (in minutes) that it takes when
   waiting for the train.

Answer each question below. Use SPSS as needed, and include the
software outputs as part of the Word document you submit.

1. What is a Q-Q plot?
2. Given a set of realized values of
   a random variable, how can a Q-Q plot be used to assess the
   distribution of the random variable?
3. Using histograms and
   Q-Q plots (except for binomial), match each random variable to one
   of the following distributions: Binomial (with N=1, P=0.7),
   Chi-square (with d.f.=20), Exponential, Lognormal, Normal, and
   Uniform.

APA format is not required, but solid academic writing is expected.

This assignment uses a grading rubric. Please review the rubric
prior to beginning the assignment to become familiar with the
expectations for successful completion.