The Central Limit Theorem: Homework is part of the collection col10555 written by Barbara Illowsky and Susan Dean.
$X$ ~
$N(\text{60},9)$ . Suppose that you form random samples of 25 from this distribution. Let
$\overline{X}$ be the random variable of averages. Let
$\mathrm{\Sigma X}$ be the random variable of sums. 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.
$\overline{X}$ ~
$P(\overline{x}<\text{60})=$
$P(\text{56}<\overline{x}<\text{62})=$
$P(\text{18}<\overline{x}<\text{58})=$
$\mathrm{\Sigma x}$ ~
Find the minimum value for the upper quartile for the sum.
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.
$N(\text{36},\frac{\text{10}}{\sqrt{\text{16}}})$
1
34.31
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.
Suppose that the weight of open boxes of cereal in a home with children is uniformly distributed from 2 to 6 pounds. We randomly survey 64 homes with children.
In words,
$X=$
$X\text{~}$
${\mu}_{X}=$
${\sigma}_{X}=$
In words,
$\mathrm{\Sigma X}=$
$\mathrm{\Sigma X}\text{~}$
Find the probability that the total weight of open boxes is less than 250 pounds.
Find the 35th percentile for the total weight of open boxes of cereal.
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 9 trials.
In words,
$\mathrm{\Sigma X}=$
$\mathrm{\Sigma X}\text{~}$
Find the probability that the total length of the 9 trials is at least 225 days.
90 percent of the total of 9 of these types of trials will last at least how long?
The total length of time for 9 criminal trials
$N(189,21)$
0.0432
162.09
According to the Internal Revenue Service, the average length of time for an individual to complete (record keep, learn, prepare, copy, assemble and send) IRS Form 1040 is 10.53 hours (without any attached schedules). The distribution is unknown. Let us assume that the standard deviation is 2 hours. Suppose we randomly sample 36 taxpayers.
In words,
$X=$
In words,
$\overline{X}=$
$\overline{X}\text{~}$
Would you be surprised if the 36 taxpayers finished their Form 1040s in an average of more than 12 hours? Explain why or why not in complete sentences.
Would you be surprised if one taxpayer finished his Form 1040 in more than 12 hours? In a complete sentence, explain why.
Questions & Answers
Do somebody tell me a best nano engineering book for beginners?
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.
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
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
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 using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
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