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Salaries for teachers in a particular elementary school district are normally distributed with a mean of $44,000 and a standard deviation of $6500. We randomly survey 10 teachers from that district.

  • In words, X = size 12{X={}} {}
  • In words, X ¯ = size 12{ {overline {X}} ={}} {}
  • X ¯ ~ size 12{ {overline {X}} "~" } {}
  • In words, ΣX = size 12{ΣX={}} {}
  • ΣX ~ size 12{ΣX "~" } {}
  • Find the probability that the teachers earn a total of over $400,000.
  • Find the 90th percentile for an individual teacher’s salary.
  • Find the 90th percentile for the average teachers’ salary.
  • If we surveyed 70 teachers instead of 10, graphically, how would that change the distribution for X ¯ size 12{ {overline {X}} } {} ?
  • If each of the 70 teachers received a $3000 raise, graphically, how would that change the distribution for X ¯ size 12{ {overline {X}} } {} ?
  • N ( 44 , 000 , 6500 10 ) size 12{ ital "Xbar" "~" N \( "44","000", { {"6500"} over { sqrt {"10"} } } \) } {}
  • N ( 440,000 , ( 10 ) ( 6500 ) ) size 12{ ital "SumX" "~" N \( "10" * "44","000", sqrt { \( "10" * "6500" \) } \) } {}
  • 0.9742
  • $52,330
  • $46,634
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The distribution of income in some Third World countries is considered wedge shaped (many very poor people, very few middle income people, and few to many wealthy people). Suppose we pick a country with a wedge distribution. Let the average salary be $2000 per year with a standard deviation of $8000. We randomly survey 1000 residents of that country.

  • In words, X = size 12{X={}} {}
  • In words, X ¯ = size 12{ {overline {X}} ={}} {}
  • X ¯ ~ size 12{ {overline {X}} "~" } {}
  • How is it possible for the standard deviation to be greater than the average?
  • Why is it more likely that the average of the 1000 residents will be from $2000 to $2100 than from $2100 to $2200?
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The average length of a maternity stay in a U.S. hospital is said to be 2.4 days with a standard deviation of 0.9 days. We randomly survey 80 women who recently bore children in a U.S. hospital.

  • In words, X = size 12{X={}} {}
  • In words, X ¯ = size 12{ {overline {X}} ={}} {}
  • X ¯ ~ size 12{ {overline {X}} "~" } {}
  • In words, ΣX = size 12{ΣX={}} {}
  • ΣX ~ size 12{ΣX "~" } {}
  • Is it likely that an individual stayed more than 5 days in the hospital? Why or why not?
  • Is it likely that the average stay for the 80 women was more than 5 days? Why or why not?
  • Which is more likely:
    • an individual stayed more than 5 days; or
    • the average stay of 80 women was more than 5 days?
  • If we were to sum up the women’s stays, is it likely that, collectively they spent more than a year in the hospital? Why or why not?
  • N ( 2 . 4, 0 . 9 80 ) size 12{ ital "Xbar" "~" N \( 2 "." 4, { {0 "." 9} over { sqrt {"80"} } } \) } {}
  • N ( 192 , 8.05 ) size 12{ ital "SumX" "~" N \( "80" * 2 "." 4, sqrt {"80"} * 0 "." 9 \) } {}
  • Individual
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In 1940 the average size of a U.S. farm was 174 acres. Let’s say that the standard deviation was 55 acres. Suppose we randomly survey 38 farmers from 1940. (Source: U.S. Dept. of Agriculture)

  • In words, X = size 12{X={}} {}
  • In words, X ¯ = size 12{ {overline {X}} ={}} {}
  • X ¯ ~ size 12{ {overline {X}} "~" } {}
  • The IQR for X ¯ size 12{ {overline {X}} } {} is from _______ acres to _______ acres.
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The stock closing prices of 35 U.S. semiconductor manufacturers are given below. (Source: Wall Street Journal )

  • 8.625
  • 30.25
  • 27.625
  • 46.75
  • 32.875
  • 18.25
  • 5
  • 0.125
  • 2.9375
  • 6.875
  • 28.25
  • 24.25
  • 21
  • 1.5
  • 30.25
  • 71
  • 43.5
  • 49.25
  • 2.5625
  • 31
  • 16.5
  • 9.5
  • 18.5
  • 18
  • 9
  • 10.5
  • 16.625
  • 1.25
  • 18
  • 12.875
  • 7
  • 12.875
  • 2.875
  • 60.25
  • 29.25

  • In words, X = size 12{X={}} {}
    • x ¯ = size 12{ {overline {x}} ={}} {}
    • s x = size 12{s rSub { size 8{x} } ={}} {}
    • n = size 12{n={}} {}
  • Construct a histogram of the distribution of the averages. Start at x = 0 . 0005 size 12{x= - 0 "." "0005"} {} . Make bar widths of 10.
  • In words, describe the distribution of stock prices.
  • Randomly average 5 stock prices together. (Use a random number generator.) Continue averaging 5 pieces together until you have 10 averages. List those 10 averages.
  • Use the 10 averages from (e) to calculate:
    • x ¯ = size 12{ {overline {x}} ={}} {}
    • s x ¯ = size 12{ {overline {s rSub { size 8{x} } }} ={}} {}
  • Construct a histogram of the distribution of the averages. Start at x = 0 . 0005 size 12{x= - 0 "." "0005"} {} . Make bar widths of 10.
  • Does this histogram look like the graph in (c)?
  • In 1 - 2 complete sentences, explain why the graphs either look the same or look different?
  • Based upon the theory of the Central Limit Theorem, X ¯ ~ size 12{ {overline {X}} "~" } {}
  • $20.71; $17.31; 35
  • Exponential distribution, X ~ Exp ( 1/20.71 ) size 12{X "~" N \( "60",9 \) } {}
  • $20.71; $11.14
  • N ( 20 . 71 , 17 . 31 5 ) size 12{ ital "Xbar" "~" N \( "20" "." "71", { {"17" "." "31"} over { sqrt {5} } } \) } {}
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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 .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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.
Bharti
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
Daniel
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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
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
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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.
Harper
Do you know which machine is used to that process?
s.
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
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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