# 5.7 Homework

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This module provides a number of homework exercises related to Continuous Random Variables.

For each probability and percentile problem, DRAW THE PICTURE!

Consider the following experiment. You are one of 100 people enlisted to take part in a study to determine the percent of nurses in America with an R.N. (registered nurse) degree. You ask nurses if they have an R.N. degree. The nurses answer “yes” or “no.” You then calculate the percentage of nurses with an R.N. degree. You give that percentage to your supervisor.

• What part of the experiment will yield discrete data?
• What part of the experiment will yield continuous data?

When age is rounded to the nearest year, do the data stay continuous, or do they become discrete? Why?

Births are approximately uniformly distributed between the 52 weeks of the year. They can be said to follow a Uniform Distribution from 1 – 53 (spread of 52 weeks).

• $X~$
• Graph the probability distribution.
• $f\left(x\right)=$
• $\mu =$
• $\sigma =$
• Find the probability that a person is born at the exact moment week 19 starts. That is, find $P\left(x=\text{19}\right)=$
• $P\left(2
• Find the probability that a person is born after week 40.
•  $P\left(\text{12}
• Find the 70th percentile.
• Find the minimum for the upper quarter.
• $X\text{~}U\left(1,\text{53}\right)$
• $f\left(x\right)=\frac{1}{\text{52}}$ where $1\le x\le \text{53}$
• 27
• 15.01
• 0
• $\frac{\text{29}}{\text{52}}$
• $\frac{\text{13}}{\text{52}}$
• $\frac{\text{16}}{\text{27}}$
• 37.4
• 40

A random number generator picks a number from 1 to 9 in a uniform manner.

• $X\text{~}$
• Graph the probability distribution.
• $f\left(x\right)=$
• $\mu =$
• $\sigma =$
• $P\left(3\text{.}5
• $P\left(x>5\text{.}\text{67}\right)=$
• $P\left(x>5\mid x>3\right)=$
• Find the 90th percentile.

The time (in minutes) until the next bus departs a major bus depot follows a distribution with $f\left(x\right)=\frac{1}{\text{20}}$ where $x$ goes from 25 to 45 minutes.

• Define the random variable. $X=$
• $X\text{~}$
• Graph the probability distribution.
• The distribution is ______________ (name of distribution). It is _____________ (discrete or continuous).
• $\mu =$
• $\sigma =$
• Find the probability that the time is at most 30 minutes. Sketch and label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement.
• Find the probability that the time is between 30 and 40 minutes. Sketch and label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement.
• $P\left(\text{25} _________. State this in a probability statement (similar to g and h ), draw the picture, and find the probability.
• Find the 90th percentile. This means that 90% of the time, the time is less than _____ minutes.
• Find the 75th percentile. In a complete sentence, state what this means. (See j .)
• Find the probability that the time is more than 40 minutes given (or knowing that) it is at least 30 minutes.
• $X\text{~}U\left(\text{25},\text{45}\right)$
• uniform; continuous
• 35 minutes
• 5.8 minutes
• 0.25
• 0.5
• 1
• 43 minutes
• 40 minutes
• 0.3333

According to a study by Dr. John McDougall of his live-in weight loss program at St. Helena Hospital, the people who follow his program lose between 6 and 15 pounds a month until they approach trim body weight. Let’s suppose that the weight loss is uniformly distributed. We are interested in the weight loss of a randomly selected individual following the program for one month. (Source: The McDougall Program for Maximum Weight Loss by John A. McDougall, M.D.)

• Define the random variable. $X=$
• $X\text{~}$
• Graph the probability distribution.
• $f\left(x\right)=$
• $\mu =$
• $\sigma =$
• Find the probability that the individual lost more than 10 pounds in a month.
• Suppose it is known that the individual lost more than 10 pounds in a month. Find the probability that he lost less than 12 pounds in the month.
• $P\left(79\right)=$ __________. State this in a probability question (similar to g and h), draw the picture, and find the probability.

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
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
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
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
1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.