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For each problem:

  • In words, define the Random Variable X size 12{X} {} .
  • List the values that X may take on.
  • Give the distribution of X . X ~
Then, answer the questions specific to each individual problem.

Six different colored dice are rolled. Of interest is the number of dice that show a “1.”

  • On average, how many dice would you expect to show a “1”?
  • Find the probability that all six dice show a “1.”
  • Is it more likely that 3 or that 4 dice will show a “1”? Use numbers to justify your answer numerically.
  • X size 12{X} {} = the number of dice that show a 1
  • 0,1,2,3,4,5,6
  • X ~ B ( 6 , 1 6 )
  • 1
  • 0.00002
  • 3 dice

More than 96 percent of the very largest colleges and universities (more than 15,000 total enrollments) have some online offerings. Suppose you randomly pick 13 such institutions. We are interested in the number that offer distance learning courses. (Source: http://en.wikipedia.org/wiki/Distance_education)

  • On average, how many schools would you expect to offer such courses?
  • Find the probability that at most 6 offer such courses.
  • Is it more likely that 0 or that 13 will offer such courses? Use numbers to justify your answer numerically and answer in a complete sentence.

A school newspaper reporter decides to randomly survey 12 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 18% of students attend Tet festivities. We are interested in the number of students who will attend the festivities.

  • How many of the 12 students do we expect to attend the festivities?
  • Find the probability that at most 4 students will attend.
  • Find the probability that more than 2 students will attend.
  • X size 12{X} {} = the number of students that will attend Tet.
  • 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
  • X ~ B(12,0.18)
  • 2.16
  • 0.9511
  • 0.3702

Suppose that about 85% of graduating students attend their graduation. A group of 22 graduating students is randomly chosen.

  • How many are expected to attend their graduation?
  • Find the probability that 17 or 18 attend.
  • Based on numerical values, would you be surprised if all 22 attended graduation? Justify your answer numerically.

At The Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 25 fencers at The Fencing Center. We are interested in the numbers that do not use the foil as their main weapon.

  • How many are expected to not use the foil as their main weapon?
  • Find the probability that six do not use the foil as their main weapon.
  • Based on numerical values, would you be surprised if all 25 did not use foil as their main weapon? Justify your answer numerically.
  • X size 12{X} {} = the number of fencers that do not use foil as their main weapon
  • 0, 1, 2, 3,... 25
  • X ~ B(25,0.40)
  • 10
  • 0.0442
  • Yes

Approximately 8% of students at a local high school participate in after-school sports all four years of high school. A group of 60 seniors is randomly chosen. Of interest is the number that participated in after-school sports all four years of high school.

  • How many seniors are expected to have participated in after-school sports all four years of high school?
  • Based on numerical values, would you be surprised if none of the seniors participated in after-school sports all four years of high school? Justify your answer numerically.
  • Based upon numerical values, is it more likely that 4 or that 5 of the seniors participated in after-school sports all four years of high school? Justify your answer numerically.

Questions & Answers

so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Collaborative statistics (custom lecture version modified by t. short). OpenStax CNX. Jul 15, 2013 Download for free at http://cnx.org/content/col11543/1.1
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