# 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.

what does nano mean?
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?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
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
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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 ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
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
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
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preparation of nanomaterial
how did you get the value of 2000N.What calculations are needed to arrive at it
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