# 15.2 Problems on random selection  (Page 5/7)

The number N of “hits” in a day on a Web site on the internet is Poisson (80). Suppose the probability is 0.10 that any hit results in a sale, is 0.30that the result is a request for information, and is 0.60 that the inquirer just browses but does not identify an interest. What is the probability of 10 or more sales? Whatis the probability that the number of sales is at least half the number of information requests (use suitable simple approximations)?

X = 0:30; Y = 0:80;PX = ipoisson(80*0.1,X); PY = ipoisson(80*0.3,Y);icalc: X Y PX PY - - - - - - - - - - - -PX10 = (X>=10)*PX' % Approximate calculation PX10 = 0.2834pX10 = cpoisson(8,10) % Direct calculation pX10 = 0.2834M = t>=0.5*u; PM = total(M.*P)PM = 0.1572

The number N of orders sent to the shipping department of a mail order house is Poisson (700). Orders require one of seven kinds of boxes, which with packing costs havedistribution

 Cost (dollars) 0.75 1.25 2 2.5 3 3.5 4 Probability 0.1 0.15 0.15 0.25 0.2 0.1 0.05

What is the probability the total cost of the $2.50 boxes is no greater than$475? What is the probability the cost of the $2.50 boxes is greater than the cost of the$3.00 boxes?What is the probability the cost of the $2.50 boxes is not more than$50.00 greater than the cost of the $3.00 boxes? Suggestion . Truncate the Poisson distributions at about twice the mean value. X = 0:400; Y = 0:300;PX = ipoisson(700*0.25,X); PY = ipoisson(700*0.20,Y);icalc Enter row matrix of X-values XEnter row matrix of Y-values Y Enter X probabilities PXEnter Y probabilities PY Use array operations on matrices X, Y, PX, PY, t, u, and PP1 = (2.5*X<=475)*PX' P1 = 0.8785M = 2.5*t<=(3*u + 50); PM = total(M.*P)PM = 0.7500 One car in 5 in a certain community is a Volvo. If the number of cars passing a traffic check point in an hour is Poisson (130), what is the expected number of Volvos? Whatis the probability of at least 30 Volvos? What is the probability the number of Volvos is between 16 and 40 (inclusive)? P1 = cpoisson(130*0.2,30) = 0.2407 P2 = cpoisson(26,16) - cpoisson(26,41) = 0.9819 A service center on an interstate highway experiences customers in a one-hour period as follows: • Northbound: Total vehicles: Poisson (200). Twenty percent are trucks. • Southbound: Total vehicles: Poisson (180). Twenty five percent are trucks. • Each truck has one or two persons, with respective probabilities 0.7 and 0.3. • Each car has 1, 2, 3, 4, or 5 persons, with probabilities 0.3, 0.3, 0.2, 0.1, 0.1, respectively Under the usual independence assumptions, let D be the number of persons to be served. Determine $E\left[D\right]$ , $\mathrm{Var}\phantom{\rule{0.166667em}{0ex}}\left[D\right]$ , and the generating function ${g}_{D}\left(s\right)$ . $T\sim$ Poisson (200*0.2 + 180*0.25 = 85), $P\sim$ Poisson (200*0.8 + 180*0.75 = 295). a = 85 b = 200*0.8 + 180*0.75b = 295 YT = [1 2]; PYT = [0.7 0.3]; EYT = dot(YT,PYT)EYT = 1.3000 VYT = dot(YT.^2,PYT) - EYT^2VYT = 0.2100 YP = 1:5;PYP = 0.1*[3 3 2 1 1];EYP = dot(YP,PYP) EYP = 2.4000VYP = dot(YP.^2,PYP) - EYP^2 VYP = 1.6400EDT = 85*EYT EDT = 110.5000EDP = 295*EYP EDP = 708.0000ED = EDT + EDP ED = 818.5000VT = 85*(VYT + EYT^2) VT = 161.5000VP = 295*(VYP + EYP^2) VP = 2183VD = VT + VP VD = 2.2705e+03NT = 0:180; % Possible alternativegNT = ipoisson(85,NT); gYT = 0.1*[0 7 3]; [DT,PDT]= gendf(gNT,gYT); EDT = dot(DT,PDT)EDT = 110.5000 VDT = dot(DT.^2,PDT) - EDT^2VDT = 161.5000 NP = 0:500;gNP = ipoisson(295,NP); gYP = 0.1*[0 3 2 2 1 1]; [DP,PDP]= gendf(gNP,gYP); % Requires too much memory ${g}_{DT}\left(s\right)=exp\left(85\left(0.7s+0.3{s}^{2}-1\right)\right)\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}{g}_{DP}\left(s\right)=exp\left(295\left(0.1\left(3s+3{s}^{2}2{s}^{3}+{s}^{4}+{s}^{5}\right)-1\right)\right)$ ${g}_{D}\left(s\right)={g}_{DT}\left(s\right){g}_{DP}\left(s\right)$ #### Questions & Answers what is the coefficient of -4× Mehri Reply -1 Shedrak the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1 Alfred Reply An investment account was opened with an initial deposit of$9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
12, 17, 22.... 25th term
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Atone
hi
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
find the 15th term of the geometric sequince whose first is 18 and last term of 387
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
If f(x) = x-2 then, f(3) when 5f(x+1) 5((3-2)+1) 5(1+1) 5(2) 10
Augustine
how do they get the third part x = (32)5/4
make 5/4 into a mixed number, make that a decimal, and then multiply 32 by the decimal 5/4 turns out to be
AJ
how
Sheref
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
hi
Ayuba
Hello
opoku
hi
Ali
greetings from Iran
Ali
salut. from Algeria
Bach
hi
Nharnhar
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Jeannette has $5 and$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
A fair die is tossed 180 times. Find the probability P that the face 6 will appear between 29 and 32 times inclusive