### MATH 318 Chapter 3 Quiz

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This is a take home quiz. Please do not write any answers on this quiz while working with someone or while consulting a reference. You are encouraged to work in groups and consult references while referring to this quiz; just take notes on scratch paper, not the quiz. You may also ask questions about the quiz during class, in office hours and at the tutoring center. If you use Excel, a table of values, or a calculator to get answers to a problem please write down the command you used, the value you looked up, or the sequence of buttons you pressed to get your answer.

Answers on this quiz should be written in your own words; copy calculations from scratch paper to this page (check your work!) and fill in your explanations without outside help. If you have any questions about this policy please ask me.

1. (10 pts) Suppose that a town has 100 residents under the age of 21, and that the ages of those residents are uniformly distributed between 0 and 20 years of age.  If a resident under the age of 21 is selected at random, what is the probability that that person is between 5 and 10 years old?  Show your work.

2. "Screen time" is the amount of time you spend looking at computer monitors, laptops, tablets, movie screens, and TV's during the day. Define the random variable x = number of hours of screen time in a day.

a) (5 pts) Is x a continuous or discrete random variable? Why?

b) (10 pts) Sketch a graph of the probability function or probability distribution function f(x). Label your axes and the interesting features (maxima, x-intercepts, etc.) of your graph.

c) (5 pts) Would you say that this random variable has a high variance? Why or why not?

3. Suppose BSU averages two weather-related closures during each spring semester, and the registrar wants to know the probability of there being more than four weather-related closures during a given semester.

a) (5 pts) Define a random variable to help answer this question.

b) (5 pts) What probability distribution would you use to answer the Registrar's question, and why?

c) (5 pts) What is the probability of more than four weather-related closures in a given semester?

d) (5 pts) Use the information provided to find the probability of there being at least one weather-related closure during a summer semester or explain why you are unable to do so.

4. The average height of a student in Professor Burgiel's MATH113 class is 65 inches. The standard deviation of student heights is 3 inches.

a) (5 pts) Is x = height of a student a discrete or continuous random variable?  Explain your reasoning.

b) (5 pts) What probability distribution would you use to answer questions about the heights of these students, and why?

c) (10 pts) What is the probability of a student in this class being between 62 and 68 inches tall?

d) (5 pts) What is the probability of a student in this class being under 60 inches tall?

5. Suppose that the Department of Transportation reports an average of 10 potholes in every 50 miles of route 495.

a) (5 pts) What is the average distance between potholes on route 495?

b) (5 pts) You wish to find the probability of two potholes being less than five miles apart.  What probability distribution will you use and why?

c) (5 pts) What is the probability of two potholes being less than five miles apart?

d) (10 pts) What is the probability that a given five mile stretch of road contains exactly two potholes?

Bonus: (5 pts) Give an example of how you might use Bayes' theorem in your chosen line of work.