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A random number N of students take a qualifying exam. A grade of 70 or more earns a pass. Suppose binomial (20, 0.3). If each student has probability 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 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 Suppose the number of Japanese visitors to Florida in a week is Poisson (500) and the number of German visitors is 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 for .
Poisson (500*0.25 = 125); Poisson (300*0.20 = 60); 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 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 Poisson (45). On incoming line 1 the messages have probability of leaving on outgoing line a and of leaving on line b. The messages coming in on line 2 have probability 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 A computer store sells Macintosh, HP, and various other IBM compatible personal computers. It has two major sources of customers:
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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