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
where we get a research paper on Nano chemistry....?
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
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?
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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