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
$X$ be the random variable representing the time it takes her to complete one review. Assume
$X$ is normally distributed. Let
$\overline{X}$ be the random variable representing the average time to complete the 16 reviews. Let
$\mathrm{\Sigma X}$ be the total time it takes Yoonie to complete all of the month’s reviews.
Distribution
Complete the distributions.
$X$ ~
$\overline{X}$ ~
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.
Find the probability that the
average of a month’s reviews will take Yoonie from 3.5 to 4.25 hrs.
$P\text{( )}=$ _______
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.
The 95th Percentile=
4.49 hours
Discussion question
What causes the probabilities in
[link] and
[link] to differ?
Questions & Answers
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
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
can nanotechnology change the direction of the face of the world
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.
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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