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1- Many countries governments wish to assess the proportion of the general populous that has certain deadly diseases. In many cases these diseases are rare and are thus very difficult to detect, even when screening many individuals. Thus a researcher proposes the following method of conducting infectious disease surveillance. Individuals are screened until the first infectious individual is observed, screening is then stopped and the proportion of infected individuals is estimated. If the 996th person screened, is the first person to be diagnosed as positive, suggest a method of estimating p, the true but unknown proportion of individuals who are infected, then use your method to estimate p in the context of this problem. Solution The random variable in the experiment follows a geometric distribution. -Geo(p) In a geometric distribution we get the expected value of x, E(X) by 1/(p) = E(X). Since from the experiment we know that E(X) = 996, we can put this into the formula to obtain p. -> 1/996 = p = 0.001 so, 0.1% of the population is infected..

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1. 70% of the students in a class passed an exam.59% of the students had completed the practice test. 48% of the students completed the practice test and passed the exam. Find the probability that a student passed the test given that the student completed the practice test. 2. An insurance company finds that 15% of their customers were in accidents this year.Of those, 65% had received a traffic ticket within the last 3 years. Of the people who had not been in an accident, 51% had received a traffic ticket within the last 3 years. Find the probability that a customer was in an accident this year given that he or she has received a traffic ticket within the last 3 years. Solution P(pass) = 0.7 P(practice) = 0.59 P(pass and practice) = 0.48 P(pass | practice) = ? P(pass | practice) = P(pass and practice)/P(practice) = 0.48/0.59 = 0.81 2) P(accident) = 0.15 P(ticket | accident) = 0.65 P(ticket|no accident) = 0.51 P(accident | ticket) = P(accident and ticket) / P(ticket) = 0.65*0.15/(0.65*0.15 + 0.51*0.85) = 0.1836.

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1. (TCO 9) Remittances of Mexican workers in the U.S. to their families in Mexico are included in the U.S. balance of payments as a debit in the section on(Points : 4) trade in services. net international transfers. financial accounts. capital accounts.Question 2.2. (TCO 9) A trade deficit means a net (Points : 4) inflow of payments for goods and services. outflow of goods and services. inflow of goods and services. excess of exports over imports.Question 3.3. (TCO 9) If a Japanese importer could buy $1,000 U.S. for 122,000 yen, the rate of exchange for $1 would be (Points : 4) 8.19 yen. 122 yen. 820 yen. 1,220 yen.Question 4.4. (TCO 9) When the exchange rate between pounds and dollars moves from $2 = 1 pound to $1 = 1 pound, we say that the dollar has (Points : 4) depreciated. appreciated. inflated. deflated.Question 5.5. (TCO 9) The monetary system for conducting international trade is usually described as a system of (Points : 4) fixed exchange rates. freely floating exchange rates. a managed gold standard. managed floating exchange rates.1. (TCO 9) Remittances of Mexican workers in the U.S. to their families in Mexico are included in the U.S. balance of payments as a debit in the section on(Points : 4) trade in services. net international transfers. financial accounts. capital accounts. Solution 1. Remittances of Mexican workers in the U.S. to their families in Mexico are included in the U.S. balance of payments as a debit in the section on \" net international transfers\". Because such remittances are unilateral transfers and shall be deducted from net international transfers in current account. 2. A trade deficit means a net \"inflow of goods and services\". It is a condition where imports of a country exceeds export of that country hence representing net inflow of goods and service. 3. If a Japanese importer could buy $1,000 U.S. for 122,000 yen, the rate of exchange for $1 would be \"122 yen\". Calculated as: $1 = 122,000 yen / $1,000 = 122 yen. 4. When the exchange rate between pounds and dollars moves from $2 = 1 pound to $1 = 1 pound, we say that the dollar has \"appreciated\". Because now with the effect of change a person would have to spend more amount of pound than before to get same amount of dollar. 5. The monetary system for conducting international trade is usually described as a system of \" managed floating exchange rates\". It is the current system in which currencies exchange flactuautes day to day..

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1. Hair stylists now serve both men and women. Management Looks magazine did a survey of mid-management people to see if there is a difference in the proportion of women and men going to a hair stylist regularly. A random sample of 50 mid-management men showed that 31 went to stylists regularly while a random sample of 36 mid-management women showed that 20 went to stylists regularly. Test the claim that there is no difference in the proportion of mid-management men and women who go to hair stylists regularly. (Use a 0.05 level of significance) Solution proportion of men = 31/50 proportion of women = 20/36 phat = (31 + 20)/(50 + 36) = 51/86 test statistic = (31/50 - 20/36)/(square root of 51/86*35/86)*square root of(1/50 + 1/36) = .6001 p value = .2742 Since p value is greater than .05, you would fail to reject the null hypothesis. There is not enough evidence to support the conclusion that there is a difference..

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1-Find the directional derivative of f(x,y)=x/y at the point (1,-1) in the direction of the vector v=(2,5) 2-Find an equation of the tangent plane to the surface xysin(z/3)=6, at the point (3,4,1), The equation should have the form g(x,y,z)=0 and the coeffecient of x shoud be 23. 3-Find equations of the tangent plane and normal line to the surface x=4y^2+2z^2-292 at the point (2,-7,7), also find the normal line? Solution f/x (x,y) = 1/y f/y (x,y)= -x/y2 f/x (1,-1) = -1 f/y (1,-1) = -1 Therefore, the gradient is f (1,-1) = - i - j = (-1,-1) --------------(1) Letu=u1i+u2jbe a unit vector.The directional derivative at (1,-1) in the direction ofuis Du f (1,-1) = (u1i+u2j) (-i-j) = -u1 - u2 directional vector u = (2,5) /29 = (2/29,5/29) = (u1,u2) ince we are still at the point (1,-1), equation (1)is still valid. We plug in our newuto obtain Duf(1,-1) = -u1 - u2 = -2/29-5/29 = 3/29.

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