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Unformatted text preview: Spring, 2004 MAT 121 MAT 121 FinalC ( 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—andleaf 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 689599.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. _IﬂE 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 Xlinked 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 Xlinked 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) tdistribution 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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