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Student learning outcome:

  • The student will compare and contrast empirical data and a theoretical distribution to determine if Terry Vogel's lap times fit a continuous distribution.


Round the relative frequencies and probabilities to 4 decimal places. Carry all other decimal answers to 2 places.

Collect the data

  1. Use the data from Terri Vogel’s Log Book . Use a Stratified Sampling Method by Lap (Races 1 – 20) and a random number generator to pick 6 lap times from each stratum. Record the lap times below for Laps 2 – 7.
    _______ _______ _______ _______ _______ _______
    _______ _______ _______ _______ _______ _______
    _______ _______ _______ _______ _______ _______
    _______ _______ _______ _______ _______ _______
    _______ _______ _______ _______ _______ _______
    _______ _______ _______ _______ _______ _______
  2. Construct a histogram. Make 5 - 6 intervals. Sketch the graph using a ruler and pencil. Scale the axes.
    Blank graph with relative frequency on the vertical axis and lap time on the horizontal axis.
  3. Calculate the following.
    • x =
    • s =
  4. Draw a smooth curve through the tops of the bars of the histogram. Use 1 – 2 complete sentences to describe the general shape of the curve. (Keep it simple. Does the graph go straight across, does it have a V-shape, does it have a hump in the middle or at either end, etc.?)

Analyze the distribution

Using your sample mean, sample standard deviation, and histogram to help, what was the approximate theoretical distribution of the data?

  • X ~
  • How does the histogram help you arrive at the approximate distribution?

Describe the data

Use the Data from the section titled "Collect the Data" to complete the following statements.

  • The IQR goes from __________ to __________.
  • IQR = __________. (IQR=Q3-Q1)
  • The 15th percentile is:
  • The 85th percentile is:
  • The median is:
  • The empirical probability that a randomly chosen lap time is more than 130 seconds =
  • Explain the meaning of the 85th percentile of this data.

Theoretical distribution

Using the theoretical distribution from the section titled "Analyse the Distribution" complete the following statements:

  • The IQR goes from __________ to __________.
  • IQR =
  • The 15th percentile is:
  • The 85th percentile is:
  • The median is:
  • The probability that a randomly chosen lap time is more than 130 seconds =
  • Explain the meaning of the 85th percentile of this distribution.

Discussion questions

  • Do the data from the section titled "Collect the Data" give a close approximation to the theoretical distibution in the section titled "Analyze the Distribution"? In complete sentences and comparing the result in the sections titled "Describe the Data" and "Theoretical Distribution", explain why or why not.

Questions & Answers

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.
Nerisha Reply

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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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