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In this module the student will explore the properties of data with an exponential distribution.

Student learning outcomes

  • The student will analyze data following the exponential distribution.


Carbon-14 is a radioactive element with a half-life of about 5730 years. Carbon-14 is said to decay exponentially. The decay rate is 0.000121 . We start with 1 gram of carbon-14. We are interested in the time (years) it takes to decay carbon-14.

Describe the data

What is being measured here?

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Are the data discrete or continuous?


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In words, define the Random Variable X size 12{X} {} .

X size 12{X} {} = Time (years) to decay carbon-14

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What is the decay rate ( m size 12{m} {} )?

m size 12{m} {} = 0.000121

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The distribution for X size 12{X} {} is:

X size 12{X} {} ~ Exp(0.000121)

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Find the amount (percent of 1 gram) of carbon-14 lasting less than 5730 years. This means, find P ( x < 5730 ) size 12{P \( X<"5730" \) } {} .

  • Sketch the graph. Shade the area of interest.
    Blank graph with vertical and horizontal axes.
  • Find the probability. P ( x < 5730 ) size 12{P \( X<"5730" \) } {} =
  • P ( x < 5730 ) size 12{P \( X<"5730" \) } {} = 0.5001
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Find the percentage of carbon-14 lasting longer than 10,000 years.

  • Sketch the graph. Shade the area of interest.
    Blank graph with horizontal and vertical axes.
  • Find the probability. P ( x > 10000 ) size 12{P \( X<"5730" \) } {} =
  • P ( x > 10000 ) size 12{P \( X<"5730" \) } {} = 0.2982
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Thirty percent (30%) of carbon-14 will decay within how many years?

  • Sketch the graph. Shade the area of interest.
    Blank graph with vertical and horizontal axes.
  • Find the value k size 12{k} {} such that P ( x < k ) = 0 . 30 size 12{P \( X<k \) =0 "." "30"} {} .
  • k size 12{k} {} = 2947.73
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Questions & Answers

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
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
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
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
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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