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MAT121-2004Spring - Spring 2004 MAT 121 MAT 121 Final-C May...

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Unformatted text preview: Spring, 2004 MAT 121 MAT 121 Final-C ( May 3, 2004 ) Name : _____________________ Student Number : Instructor : ********** 1. There are 7 problems and 8 pages in this booklet. 2. Show all of your work and label your answers clearly. Unexplained answers will not get the full credit. Even if you perform all your calculations on your calculator, you MUST indicate what formula/ procedures you are using. ********** 1. (19 points) Here are data on the percent of sugar in some popular breakfast cereals: 103040353813519482956567 (a) Construct the stem—and-leaf plot and describe the overall shape of the distribution: is it roughly symmetric, skewed to the right, or skewed to the left? (b) Find the five number summary of the distribution and construct the boxplot. For the first and third quartiles, indicate their positions, L. (c) With no further computations you should be able to decide which of the following eight state- ments about these values are valid and which are not valid. Choose all the valid statements and explain why they are valid. (i ) mean > median (ii) mean < median (iii) mean % median (iv) The mean would be a good choice to represent the center. (v) The median would be a good choice to represent the center. (vi ) The 68-95-99.T rule can be applied to this data set. [0 2. (11 points) The following data summarizes the distribution of blood types (ABO type and Rh type) for 300 subjects randomly selected from a large population. Give your answers to three decimal places. _Ifl--E Rh positive 82 89 54 20 Rh negative 13 27 7 8 (a) If a subject is randomly selected from this population, find the probability of getting someone who has a type AB blood. (b) If a donor is randomly selected from this population, find the probability of getting someone who has a type ”AB” as well as ”Rh negative”. (c) If a donor is randomly selected from this population, find the probability that he/she has ”Rh negative” given that his/ her blood type is ”AB.” (d) If a donor is randomly selected from this population, find the probability that he/ she has ”AB” given that his/ her blood type is ”Rh negative.” (e) Let A be the event that a randomly selected subject has a type ”AB”, and B be the event that a randomly selected subject has ”Rh negative”. Are the events A and B disjoint? Are they independent? Provide mathematical justifications for your answers. 3. (13 points) In a survey recently done by USA TODAY/CNN/Gallup Poll (USA Today, April 19, 2004), 1003 randomly selected national adults are surveyed. Asked who they would be more likely to vote for, J. Kerry or G. W. Bush, 46% of them said ”Kerry”. (a) Noting that each individual’s response is either Bush, Kerry, Neither or No opinion, identify the level of measurement (nominal, ordinal, interval, ratio) for each individual response. (b) USA Today reports that ”For the result that 46% preferred ”Kerry” among the total sample of 1003 national adults, one can say with 95% confidence that the margin of sampling error is 3 percentage points.” Verify that the margin of error is 3 percentage points. (c) If USA Today likes to decrease the margin of error to 0.015 with the 95% level of confidence, how large sample would they need to survey? Use 15 reported in the current survey. 4. (15 points) A genetics expert has determined that for certain couples, there is a 0.24 probability that any child will have an X-linked recessive disorder. (a) Consider a couple from this population who plans to have five children. Find the probability that at least one of their five children have an X-linked recessive disorder. (b) Consider a couple from this population who plans to have five children. Use the binomial formula to compute the probability that exactly 3 of their five children have an X—linked recessive disorder. (c) Use the normal distribution to approximate the probability that among 200 such children selected from this population, at least 65 have the X—linked recessive disorder. Be sure to make a continuity correction. 5. (18 points) The US. Marine Corps requires that men have heights between 64 inches and 78 inches. Assume that heights of men are normally distributed with a mean of 68.0 inches and a standard deviation of 2.7 inches. (a) Find the percentage of men meeting those height requirement. (b) If the Secretary of Defense likes to change the requirement so that only the shortest 3% and tallest 3% of all men are rejected, what are the new minimum and maximum height requirement? Round your final answers to one decimal place. (c) If 32 men are randomly selected, find the probability that they mean height is greater than 67.0 inches. 6. (18 points) The mean replacement time for a random sample of 19 washing machines is 9.5 years and the standard deviation is 2.4 years. (a) Construct a 90% confidence interval for the mean replacement time. (b) Construct a 99% confidence interval for the standard deviation, 0, of the replacement times of all washing machines of this type. 7. (6 points) (a) Suppose you wish to construct a 98% confidence interval for ,u with a sample of size 41. If it is known that 0 = 10 and the population appears to be very skewed, choose which one of the following critical values should be used: (i) ta/g = 2.423 (ii) 20/3 : 2.33 (iii) za/g = 1.96 (iv) neither (b) Match each one of the following distributions to the appropriate density curve. (i) uniform distribution (ii) standard normal distribution (iii) X2 distribution with 3 degrees of freedom ( iv) t-distribution with 5 degrees of freedom (3) (2) (c) (Bonus) Suppose that based on a sample of 50 packages randomly selected, the following interval is obtained as a 95% confidence interval for mean weight: 14.7 < [1. < 15.9. Which of the following statements is a valid interpretation of this confidence interval? (i) If 100 different samples of size 50 were selected and, based on each sample, a confidence interval were constructed, exactly 95 of these confidence intervals would contain the true value of 11. (ii ) There is a 95% chance that the true value of ,u lies between 14.7 and 15.9. (iii) If many different samples of size 50 were selected and, based on each sample, a confidence interval were constructed, 95% of the time the true value ,u. lie between 14.7 and 15.9. (iv) If many different samples of size 50 were selected and, based on each sample, a confidence interval were constructed, in the long run 95% of the confidence intervals would contain the true value of 11.. ...
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