<< Chapter < Page Chapter >> Page >

Try it

According to a Gallup poll, 60% of American adults prefer saving over spending. Let X = the number of American adults out of a random sample of 50 who prefer saving to spending.

  1. What is the probability distribution for X ?
  2. Use your calculator to find the following probabilities:
    1. the probability that 25 adults in the sample prefer saving over spending
    2. the probability that at most 20 adults prefer saving
    3. the probability that more than 30 adults prefer saving
  3. Using the formulas, calculate the (i) mean and (ii) standard deviation of X .
  1. X B (50, 0.6)
  2. Using the TI-83, 83+, 84 calculator with instructions as provided in [link] :
    1. P ( x = 25) = binompdf(50, 0.6, 25) = 0.0405
    2. P ( x ≤ 20) = binomcdf(50, 0.6, 20) = 0.0034
    3. P ( x >30) = 1 - binomcdf(50, 0.6, 30) = 1 – 0.5535 = 0.4465
    1. Mean = np = 50(0.6) = 30
    2. Standard Deviation = n p q = 50 ( 0.6 ) ( 0.4 ) ≈ 3.4641

The lifetime risk of developing pancreatic cancer is about one in 78 (1.28%). Suppose we randomly sample 200 people. Let X = the number of people who will develop pancreatic cancer.

  1. What is the probability distribution for X ?
  2. Using the formulas, calculate the (i) mean and (ii) standard deviation of X .
  3. Use your calculator to find the probability that at most eight people develop pancreatic cancer
  4. Is it more likely that five or six people will develop pancreatic cancer? Justify your answer numerically.
  1. X B (200, 0.0128)
    1. Mean = np = 200(0.0128) = 2.56
    2. Standard Deviation = n p q  =   (200)(0 .0128)(0.9872) 1. 5897
  2. Using the TI-83, 83+, 84 calculator with instructions as provided in [link] :
    P ( x ≤ 8) = binomcdf(200, 0.0128, 8) = 0.9988
  3. P ( x = 5) = binompdf(200, 0.0128, 5) = 0.0707
    P ( x = 6) = binompdf(200, 0.0128, 6) = 0.0298
    So P ( x = 5)> P ( x = 6); it is more likely that five people will develop cancer than six.

Try it

During the 2013 regular NBA season, DeAndre Jordan of the Los Angeles Clippers had the highest field goal completion rate in the league. DeAndre scored with 61.3% of his shots. Suppose you choose a random sample of 80 shots made by DeAndre during the 2013 season. Let X = the number of shots that scored points.

  1. What is the probability distribution for X ?
  2. Using the formulas, calculate the (i) mean and (ii) standard deviation of X .
  3. Use your calculator to find the probability that DeAndre scored with 60 of these shots.
  4. Find the probability that DeAndre scored with more than 50 of these shots.
  1. X ~ B (80, 0.613)
    1. Mean = np = 80(0.613) = 49.04
    2. Standard Deviation = n p q = 80 ( 0.613 ) ( 0.387 ) 4.3564
  2. Using the TI-83, 83+, 84 calculator with instructions as provided in [link] :
    P ( x = 60) = binompdf(80, 0.613, 60) = 0.0036
  3. P ( x >50) = 1 – P ( x ≤ 50) = 1 – binomcdf(80, 0.613, 50) = 1 – 0.6282 = 0.3718

The following example illustrates a problem that is not binomial. It violates the condition of independence. ABC College has a student advisory committee made up of ten staff members and six students. The committee wishes to choose a chairperson and a recorder. What is the probability that the chairperson and recorder are both students? The names of all committee members are put into a box, and two names are drawn without replacement . The first name drawn determines the chairperson and the second name the recorder. There are two trials. However, the trials are not independent because the outcome of the first trial affects the outcome of the second trial. The probability of a student on the first draw is 6 16 . The probability of a student on the second draw is 5 15 , when the first draw selects a student. The probability is 6 15 , when the first draw selects a staff member. The probability of drawing a student's name changes for each of the trials and, therefore, violates the condition of independence.

Questions & Answers

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
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
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
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?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
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
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Introduction to statistics i - stat 213 - university of calgary - ver2015revb. OpenStax CNX. Oct 21, 2015 Download for free at http://legacy.cnx.org/content/col11874/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introduction to statistics i - stat 213 - university of calgary - ver2015revb' conversation and receive update notifications?

Ask