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A random number N of students take a qualifying exam. A grade of 70 or more earns a pass. Suppose N binomial (20, 0.3). If each student has probability p = 0 . 7 of making 70 or more, what is the probability all will pass? Ten or more will pass?

gN = ibinom(20,0.3,0:20); gY = [0.3 0.7]; gendDo not forget zero coefficients for missing powers Enter gen fn COEFFICIENTS for gN gNEnter gen fn COEFFICIENTS for gY gY Results are in N, PN, Y, PY, D, PD, PMay use jcalc or jcalcf on N, D, P To view the distribution, call for gD.Pall = (D==20)*PD' Pall = 2.7822e-14pall = (0.3*0.7)^20 % Alternate: use D binomial (pp0) pall = 2.7822e-14P10 = (D>= 10)*PD' P10 = 0.0038
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Five hundred questionnaires are sent out. The probability of a reply is 0.6. The probability that a reply will be favorable is 0.75. What is the probability of at least200, 225, 250 favorable replies?

n = 500; p = 0.6;p0 = 0.75; D = 0:500;PD = ibinom(500,p*p0,D); k = [200 225 250]; P = zeros(1,3);for i = 1:3 P(i) = (D>=k(i))*PD'; enddisp(P) 0.9893 0.5173 0.0140
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Suppose the number of Japanese visitors to Florida in a week is N 1 Poisson (500) and the number of German visitors is N 2 Poisson (300). If 25 percent of the Japanese and 20 percent of the Germans visit Disney World,what is the distribution for the total number D of German and Japanese visitors to the park? Determine P ( D k ) for k = 150 , 155 , , 245 , 250 .

J D Poisson (500*0.25 = 125); G D Poisson (300*0.20 = 60); D Poisson (185).

k = 150:5:250; PD = cpoisson(185,k); disp([k;PD]') 150.0000 0.9964155.0000 0.9892 160.0000 0.9718165.0000 0.9362 170.0000 0.8736175.0000 0.7785 180.0000 0.6532185.0000 0.5098 190.0000 0.3663195.0000 0.2405 200.0000 0.1435205.0000 0.0776 210.0000 0.0379215.0000 0.0167 220.0000 0.0067225.0000 0.0024 230.0000 0.0008235.0000 0.0002 240.0000 0.0001245.0000 0.0000 250.0000 0.0000
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A junction point in a network has two incoming lines and two outgoing lines. The number of incoming messages N 1 on line one in one hour is Poisson (50); on line 2 the number is N 2 Poisson (45). On incoming line 1 the messages have probability p 1 a = 0 . 33 of leaving on outgoing line a and 1 - p 1 a of leaving on line b. The messages coming in on line 2 have probability p 2 a = 0 . 47 of leaving on line a. Under the usual independence assumptions, what is the distribution of outgoing messages on line a?What are the probabilities of at least 30, 35, 40 outgoing messages on line a?

m1a = 50*0.33; m2a = 45*0.47; ma = m1a + m2a; PNa = cpoisson(ma,[30 35 40]) PNa = 0.9119 0.6890 0.3722
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A computer store sells Macintosh, HP, and various other IBM compatible personal computers. It has two major sources of customers:

  1. Students and faculty from a nearby university
  2. General customers for home and business computing. Suppose the following assumptions are reasonable for monthly purchases.
  • The number of university buyers N 1 Poisson (30). The probabilities for Mac, HP, others are 0.4, 0.2, 0.4, respectively.
  • The number of non-university buyers N 2 Poisson (65). The respective probabilities for Mac, HP, others are 0.2, 0.3, 0.5.
  • For each group, the composite demand assumptions are reasonable, and the two groups buy independently.

What is the distribution for the number of Mac sales? What is the distribution for the total number of Mac and Dell sales?

Mac sales Poisson (30*0.4 + 65*0.2 = 25); HP sales Poisson (30*0.2 + 65*0.3 = 25.5); total Mac plus HP sales Poisson(50.5).

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Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
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.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
A fair die is tossed 180 times. Find the probability P that the face 6 will appear between 29 and 32 times inclusive
Samson Reply

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Source:  OpenStax, Applied probability. OpenStax CNX. Aug 31, 2009 Download for free at http://cnx.org/content/col10708/1.6
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