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1 MAT 55-0/0 Test (Sections 4.-4., , 6., & 6.) REVIEW Spring 04 Name Date Section (Lab M-0, W-0) **Please be sure to show your work, or provide explanations for any questions that require it, so that you may receive any available partial credit!!** MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the Provide an appropriate response. ) ) A history instructor has given the same pretest and the same final examination each semester. He is interested in determining if there is a relationship between the scores of the two tests. He computes the linear correlation coefficient and notes that it is.5. What does this correlation coefficient value tell the instructor? A) The correlation is something other than linear. B) There is a strong positive correlation between the tests. C) The history instructor has made a computational error. D) There is a strong negative correlation between the tests. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the ) ) In an area of the Great Plains, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per acre). Calculate the linear correlation coefficient. Use your calculator! Rainfall (in inches), x.4 Yield (bushels per acre), y ) ) A medical researcher wishes to determine if there is a relationship between the number of prescriptions written by medical professionals, per 00, children and the child's age. She surveys all the pediatrician's in a geographical region to collect her data. What is the response (dependent) variable? 4) 4) For a random sample of 0 countries, the linear correlation coefficient between the infant mortality rate and the average number of cars per capita was found to be r = What does this imply? Does this suggest that if people buy more cars, this could lower the infant mortality rate? Why or why not? What is a likely lurking variable?
2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the 5) 5) The data below are the final exam scores of 0 randomly selected history students and the number of hours they slept the night before the exam. Find the equation of the regression line for the given data. What would be the predicted score for a history student who slept 5 hours the previous night? Is this a reasonable question? Round your predicted score to the nearest whole number. Round the regression line values to the nearest hundredth. Hours, x Scores, y A) ^y= -5.04x + 56.; -0; No, it is not reasonable. B) ^y= -5.04x + 56.; -0; Yes, it is reasonable. C) ^y= 5.04x + 56.; ; Yes, it is reasonable. D) ^y= 5.04x + 56.; ; No, it is not reasonable. 5 hours is well outside the scope of the model. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the 6) 6) In an area of the Great Plains, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per acre). Compute the sum of the squared residuals of the least-squares line for the given data. It is strongly advised that you use your graphing calculator and list capabilities to do this problem! Rain fall (in inches), x Yield (bushels per acre), y ) 7) Calculate the coefficient of determination to the nearest thousandth, given that the linear correlation coefficient, r, is 0.7. What does this tell you about the explained variation and the unexplained variation of the data about the regression line? ) The table below represents a random sample of the number of deaths per 00 cases for a ) certain illness over time. If a person infected with this illness is randomly selected from all infected people, find the probability that the person lives -4 years after diagnosis. Express your answer as a simplified fraction and as a decimal. Years after Diagnosis Number deaths ) 9) A single die is rolled twice. The set of 6 equally likely outcomes is {(, ), (, ), (, ), (, 4), (, 5), (, 6), (, ), (, ), (, ), (, 4), (, 5), (, 6), (, ), (, ), (, ), (, 4), (, 5), (, 6), (4, ), (4, ), (4, ), (4, 4), (4, 5), (4, 6), (5, ), (5, ), (5, ), (5, 4), (5, 5), (5, 6), (6, ), (6, ), (6, ), (6, 4), (6, 5), (6, 6)}. Find the probability of getting two numbers whose sum is greater than
3 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the 0) 0) The probability of an outcome is obtained by dividing the frequency of occurrence of an event by the number of trials of the experiment. A) Conditional B) Subjective C) Empirical D) Classical SHORT ANSWER. Write the word or phrase that best completes each statement or answers the Solve the problem. ) ) The events A and B are mutually exclusive. If P(A) = 0. and P(B) = 0., what is P(A and B)? ) Given that P(A or B) = 4, P(A) =, and P(A and B) =, find P(B). Express the probability 9 ) as a simplified fraction. ) The table lists the drinking habits of a group of college students. If a student is chosen at ) random, find the probability of getting someone who is a man or a non-drinker. Round your answer to three decimal places. Sex Non-drinker Regular Drinker Heavy Drinker Total Man Woman Total 5 6 4) 4) If one card is drawn from a standard 5 card playing deck, determine the probability of getting a jack, a three, a club or a diamond. Round to the nearest hundredth. 5) The overnight shipping business has skyrocketed in the last ten years. The single greatest 5) predictor of a company's success has been proven time and again to be customer service. A study was conducted to study the customer satisfaction levels for one overnight shipping business. In addition to the customer's satisfaction level, the customers were asked how often they used overnight shipping. The results are shown below in the following table. What is the probability that a respondent did not have a high level of satisfaction with the company? Round the the nearest hundredth. Satisfaction level Frequency of Use High Medium Low TOTAL < per month per month > 5 per month TOTAL ) 6) A single die is rolled twice. Find the probability of getting a the first time and a 6 the second time. Express the probability as a simplified fraction.
4 7) 7) A bag contains 0 white, blue, red, 7 yellow, and green wooded balls. A ball is selected from the bag, its color noted, then replaced. You then draw a second ball, note its color and then replace the ball. What is the probability of selecting one white ball and one blue ball? Round to the nearest ten-thousandth. Provide an appropriate response. ) ) You toss a fair coin 5 times. What is the probability of at least one head? Round to the nearest ten-thousandth. Find the indicated probability. Give your answer as a simplified fraction. 9) The managers of a corporation were surveyed to determine the background that leads to 9) a successful manager. Each manager was rated as being either a good, fair, or poor manager by his/her boss. The manager's educational background was also noted. The data appear below. Given that a manager is only a fair manager, what is the probability that this manager has a college degree? Educational Background Manager Rating H. S. Degree Some College College Degree Master's or Ph.D. Totals Good Fair Poor Totals Find the indicated probability. If necessary, round to three decimal places. 0) 0) Suppose that E and F are two events and that N(E and F) = 0 and N(E) = 0. What is P( F E)? Provide an appropriate response. Express your answer as a simplified fraction unless otherwise noted. ) ) There are 4 chocolates in a box, all identically shaped. There 6 are filled with nuts, 0 with caramel, and are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting nut candies. ) ) CampusFest is a student festival where local businesses come on campus to sell their goods to students at vastly reduced prices. As part of a give-away promotion, a local cellular phone company gave away 500 cellular phones to students who signed up for their calling service. Unbeknownst to the company is that 0 of these cellular phones were faulty and will cause a small explosion when dialed outside the local calling area. Suppose you and your roommate each received one of the giveaway phones. Find the probability that both of you received faulty phones. Round to five decimal places when necessary. ) ) Assume that P(A) = 0.7 and P(B) = 0.. If A and B are independent, find P(A and B). Classify the following random variable according to whether it is discrete or continuous. 4) 4) the pressure of water coming out of a fire hose 4
5 5) 5) the number of goals scored in a hockey game Provide an appropriate response. 6) 6) Consider the discrete probability distribution to the right when answering the following Find the probability that x exceeds 4. x 4 7 P(x) 0.7? ) 7) The random variable x represents the number of boys in a family of three children. Assuming that boys and girls are equally likely, (a) construct a probability distribution, and (b) graph the probability histogram. The sample space for this event "HAVING THREE CHILDREN" is S = {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG} 0 X P(X = x) ) ) Calculate the mean for the discrete probability distribution shown here. x 4 5 P(x) ) A dice game involves throwing three dice and betting on one of the six numbers that are 9) on the dice. The game costs $4 to play, and you win if the number you bet appears on any of the dice. The distribution for the outcomes of the game (including the profit) is shown below: Number of dice with your number Profit Probability of Observing 0 -$4 5/6 $4 75/6 $6 5/6 $ /6 Find your expected profit from playing this game. 5
6 0) 0) Fifty percent of the people that use the Internet order something online. Find the probability that only four of 9 Internet users will order something online. HINT: Binomial PDF ) ) A recent survey found that 7% of all adults over 50 wear sunglasses for driving. In a random sample of 60 adults over 50, what is the mean and standard deviation of those that wear sunglasses? HINT: Binomial PDF ) ) A quiz consists of 0 multiple choice questions, each with five possible answers, one of which is correct. To pass the quiz a student must get 60% or better on the quiz. If a student randomly guesses, what is the probability that the student will pass the quiz? HINT: Binomial PDF 6
7 Answer Key Testname: UNTITLED ) C ) 0.9 ) Age of the child 4) A negative correlation exists between the infant mortality rate and the number of cars per capita but this is an example of correlation not causation. If people buy more cars, this is unlikely to lead to a decrease in the infant mortality rate. A likely lurking variable is wealth and this lurking variable accounts for the negative correlation. More affluent countries tend to have both more cars per capita and lower infant mortality rates. 5) D 6) 7.9 7) The coefficient of determination, R, = That is, 70.% of the variation is explained and 9.9% of the variation is unexplained. ) 5 00 ; 0.5 9) 6 0) C ) 0 ) 7 7 ) ) 0.5 5) 0.4 6) 6 7) ) ) 4 7 0) 0.5 ) 5 9 ) ) 0.4 4) continuous 5) discrete 6) 0.4 7
8 Answer Key Testname: UNTITLED 7) (a) x P(x) 0 (b) ) µ = x p(x) = (0.) + 4(0.) + 5(0.) + (0.) = 4.7 9) -$0.46 0) 0.46 ) mean: 4.6; standard deviation: ) 0.006
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