# 7.1 Homework: clt (modified r. bloom)

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Homework problems for Central Limit Theorem for the textbook collection Collaborative Statistics by Susan Dean and Dr. Barbara Illowsky; their original module has been modified to include more questions about CLT for means and eliminate questions about CLT for sums.

$X$ ~ $N\left(\text{60},9\right)$ . Suppose that you form random samples of 25 from this distribution. Let $\overline{X}$ be the random variable of averages. For c - f , sketch the graph, shade the region, label and scale the horizontal axis for $\overline{X}$ , and find the probability.

• Sketch the distributions of $X$ and $\overline{X}$ on the same graph.
• $\overline{X}$ ~
• $P\left(\overline{X}<\text{60}\right)=$
• Find the 30th percentile.
• $P\left(\text{56}<\overline{X}<\text{62}\right)=$
• $P\left(\text{18}<\overline{X}<\text{58}\right)=$
• Find the minimum value for the upper quartile.
• $\text{Xbar}\text{~}N\left(\text{60},\frac{9}{\sqrt{\text{25}}}\right)$
• 0.5000
• 59.06
• 0.8536
• 0.1333
• 61.214

Determine which of the following are true and which are false. Then, in complete sentences, justify your answers.

• When the sample size is large, the mean of $\overline{X}$ is approximately equal to the mean of $X$ .
• When the sample size is large, $\overline{X}$ is approximately normally distributed.
• When the sample size is large, the standard deviation of $\overline{X}$ is approximately the same as the standard deviation of $X$ .

The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about 10. Suppose that 16 individuals are randomly chosen.

Let $\overline{X}=$ average percent of fat calories.

• $\overline{X}\text{~}$ ______ ( ______ , ______ )
• For the group of 16, find the probability that the average percent of fat calories consumed is more than 5. Graph the situation and shade in the area to be determined.
• Find the first quartile for the average percent of fat calories.
• $N\left(\text{36},\frac{\text{10}}{\sqrt{\text{16}}}\right)$
• 1
• 34.31

Previously, De Anza statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a mean of $0.88. Suppose that we randomly pick 25 daytime statistics students. • In words, $X=$ • $X\text{~}$ • In words, $\overline{X}=$ • $\overline{X}\text{~}$ ______ ( ______ , ______ ) • Find the probability that an individual had between$0.80 and $1.00. Graph the situation and shade in the area to be determined. • Find the probability that the average of the 25 students was between$0.80 and \$1.00. Graph the situation and shade in the area to be determined.
• Explain the why there is a difference in (e) and (f).

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls.

• If $\overline{X}=$ average distance in feet for 49 fly balls, then $\overline{X}\text{~}$ _______ ( _______ , _______ )
• What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for $\overline{X}$ . Shade the region corresponding to the probability. Find the probability.
• Find the 80th percentile of the distribution of the average of 49 fly balls.
• $N\left(\text{250},\frac{\text{50}}{\sqrt{\text{49}}}\right)$
• 0.0808
• 256.01 feet

Question removed from textbook.

Note: Problem has been changed from original version of textbook.

Suppose that the duration of a particular type of criminal trial is known to have a mean of 21 days and a standard deviation of 7 days. We randomly sample 25 trials.

• Find the probability that the average length of the 25 trials is at least 24 days.
• Find the 10th percentile for the average length for samples of 25 trials of this type.
• Answer: 0.0161
• Answer: 19.2 days

#### Questions & Answers

how can chip be made from sand
Eke Reply
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Almas
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
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Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
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Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
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da
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Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
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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
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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
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 homework book: custom version modified by r. bloom. OpenStax CNX. Dec 23, 2009 Download for free at http://legacy.cnx.org/content/col10619/1.2
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