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Use the Initial Public Offering data (see “Table of Contents) to do this problem.

  • In words, X = size 12{X={}} {}
    • μ X = size 12{μ rSub { size 8{x} } ={}} {}
    • σ X = size 12{σ rSub { size 8{x} } ={}} {}
    • n = size 12{n={}} {}
  • Construct a histogram of the distribution. Start at x = 0 . 50 size 12{x= - 0 "." "50"} {} . Make bar widths of $5.
  • 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 15 averages. List those 15 averages.
  • Use the 15 averages from (e) to calculate the following:
    • 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 . 50 size 12{x= - 0 "." "50"} {} . Make bar widths of $5.
  • Does this histogram look like the graph in (c)? Explain any differences.
  • 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}} "~" } {}
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Try these multiple choice questions (exercises19 - 23).

The next two questions refer to the following information: The time to wait for a particular rural bus is distributed uniformly from 0 to 75 minutes. 100 riders are randomly sampled to learn how long they waited.

The 90th percentile sample average wait time (in minutes) for a sample of 100 riders is:

  • 315.0
  • 40.3
  • 38.5
  • 65.2

B

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Would you be surprised, based upon numerical calculations, if the sample average wait time (in minutes) for 100 riders was less than 30 minutes?

  • Yes
  • No
  • There is not enough information.

A

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Which of the following is NOT TRUE about the distribution for averages?

  • The mean, median and mode are equal
  • The area under the curve is one
  • The curve never touches the x-axis
  • The curve is skewed to the right

D

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The next three questions refer to the following information: The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of $4.59 and a standard deviation of $0.10. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 16 gas stations.

The distribution to use for the average cost of gasoline for the 16 gas stations is

  • X ~ N ( 4.59 , 0.10 )
  • X ~ N ( 4.59 , 0.10 16 )
  • X ~ N ( 4.59 , 0.10 16 )
  • X ~ N ( 4.59 , 16 0.10 )

B

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What is the probability that the average price for 16 gas stations is over $4.69?

  • Almost zero
  • 0.1587
  • 0.0943
  • Unknown

A

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Find the probability that the average price for 30 gas stations is less than $4.55.

  • 0.6554
  • 0.3446
  • 0.0142
  • 0.9858
  • 0

C

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For the Charter School Problem (Example 6) in Central Limit Theorem: Using the Central Limit Theorem , calculate the following using the normal approximation to the binomial.

  • Find the probability that less than 100 favor a charter school for grades K - 5.
  • Find the probability that 170 or more favor a charter school for grades K - 5.
  • Find the probability that no more than 140 favor a charter school for grades K - 5.
  • Find the probability that there are fewer than 130 that favor a charter school for grades K - 5.
  • Find the probability that exactly 150 favor a charter school for grades K - 5.
If you either have access to an appropriate calculator or computer software, try calculating these probabilities using the technology. Try also using the suggestion that is at the bottom of Central Limit Theorem: Using the Central Limit Theorem for finding a website that calculates binomial probabilities.

  • 0.0162
  • 0.0268

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Four friends, Janice, Barbara, Kathy and Roberta, decided to carpool together to get to school. Each day the driver would be chosen by randomly selecting one of the four names. They carpool to school for 96 days. Use the normal approximation to the binomial to calculate the following probabilities. Round the standard deviation to 4 decimal places.

  • Find the probability that Janice is the driver at most 20 days.
  • Find the probability that Roberta is the driver more than 16 days.
  • Find the probability that Barbara drives exactly 24 of those 96 days.
If you either have access to an appropriate calculator or computer software, try calculating these probabilities using the technology. Try also using the suggestion that is at the bottom of Central Limit Theorem: Using the Central Limit Theorem for finding a website that calculates binomial probabilities.

  • 0.2047
  • 0.9615
  • 0.0938

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**Exercise 24 contributed by Roberta Bloom

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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
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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