7.5 Practice: central limit theorem (modified r. bloom)

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This module contains practice problems for the Central Limit Theorem from Collaborative Statistics by Susan Dean and Dr. Barbara Illowsky. The problems relating to Central Limit Theorem for averages have not been changed in this module. The problems relating to Central Limit Theorem for sums have been removed from this module.

Student learning outcomes

  • The student will explore the properties of data through the Central Limit Theorem.

Given

Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately 4 hours each to do with a population standard deviation of 1.2 hours. Let X size 12{X} {} be the random variable representing the time it takes her to complete one review. Assume X size 12{X} {} is normally distributed. Let X ¯ size 12{ {overline {X}} } {} be the random variable representing the average time to complete the 16 reviews. Let ΣX size 12{ΣX} {} be the total time it takes Yoonie to complete all of the month’s reviews.

Distribution

Complete the distributions.

  1. X ~
  2. X ~

Graphing probability

For each problem below:

  • Sketch the graph. Label and scale the horizontal axis. Shade the region corresponding to the probability.
  • Calculate the value.

Find the probability that one review will take Yoonie from 3.5 to 4.25 hours.

  • Empty normal distribution curve graph with x-axis of X.
  • P ( size 12{P \( } {} ________ < X < size 12{<X<} {} ________ ) = size 12{ \) ={}} {} _______

  • 3.5, 4.25, 0.2441

Find the probability that the average of a month’s reviews will take Yoonie from 3.5 to 4.25 hrs.

  • Empty normal distribution curve graph for the average.
  • P ( ) = _______

  • 0.7499
  • When calculating the standard deviation for the mean using the Central Limit Theorem in this problem, the sample size is n = 16, the number of reviews she completes in a month.

Find the 95th percentile for the average time to complete one month’s reviews.

  • Empty normal distribution curve graph for the average.
  • The 95th Percentile=

  • 4.49 hours

Discussion question

What causes the probabilities in [link] and [link] to differ?

Questions & Answers

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
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
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 version modified by r. bloom. OpenStax CNX. Nov 15, 2010 Download for free at http://legacy.cnx.org/content/col10617/1.4
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