MATH 318, Chapter 3 Quiz

Name:
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 and using scratch paper. 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.

Please do not write answers on this paper while viewing a web page or working with a helper. I want your answers to be written in your own words; you should copy your equations 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. (20 points) Define the random variable x to be the time you get home on Thursday.
    a) Is x a discrete or continuous random variable? Explain.

     

     

     

     

     

    b) Sketch a graph of the probability function f(x). Explain how you determined the shape of the graph.

     

     

     

     

     

  2. (20 points) The table below gives the size of the freshman class entering BSC for the past several years.

    Class of 2005200620072008 2009201020112012 20132014
    Size 1178129713041305 1332136115841502 14791460
                  
                  

    a) Compute the expected value of the size of the freshman class. (Assume each size listed above is equally likely.)

     

     

     

     

     

    b) Compute the standard deviation of the size of the freshman class.

     

     

     

     

     

    c) Based on your answers to part (a) and (b), would you say that the size of the freshman class at BSC was extremely variable or fairly constant over the last ten years? Explain your reasoning.

     

     

     

     

  3. (20 points) The U.S. Air Force has designed a missile detection system which will detect 19 out of 20 incoming missiles. If one early warning system is good, two must be better; "how much better?".

    a) What is the probability that 1 detection system will detect an incoming missile?

     

     

    b) If 2 detection systems are installed in the same area and operate independently, what is the probability that at least 1 of the systems will detect the missile? (Check that your answer makes sense!)

     

     

     

     

     

    c) If 3 systems are installed, what is the probability that at least 1 of the systems detects the missile?

     

     

     

     

     

    d) How many detection systems would you recommend operating? Why?

  4. (20 points) Suppose the average height of a female freshman at BSU is 65 inches and the standard deviation is 5 inches. Define a random variable x whose value is the height of a randomly selected freshwoman.

    a) How would you model x? (Binomial, poisson, uniform, normal, exponential or other?)

     

     

     

     

    b) Use that model to estimate the percentage of female freshmen under 60 inches tall.

     

     

     

     

     

    c) Fill in the blank: 90% of female freshmen at BSU are over _________________ inches tall. Show your work below.

     

     

     

     

  5. (20 points) Between 4 and 9 PM, cars place orders at the drive through window of the Tiki Takeout restaurant once every 5 minutes. The worker who processes those orders gets a ten minute break every two hours.

    a) What is the probability of receiving 20 drive through orders in one hour?

     

     

     

     

     

    b) What is the probability of there being a ten minute gap between orders?

     

     

     

     

     

    c) Calculate the probability of receiving fewer than 2 orders in ten minutes.

     

     

     

     

     

    Bonus (5 points) The probability distribution function for the amount of time Professor Burgiel exercises every morning is

    f(x) = 11 - .5 * x

    when x is between 20 and 22 minutes and 0 for all other values of x. Compute the probability that Professor Burgiel exercised for more than 21 minutes this morning.