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About 102926 results. 1294 free access solutions
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| m102670 | The game of craps is played by rolling two balanced dice. A first roll of a sum of 7 or 11 wins; and a first roll of a sum of 2, 3, or 12 loses. To win with any other first sum, that sum must be repeated before a sum of 7 is thrown. It can be shown that the probability is 0.493 that a player wins a game of craps. Suppose we consider a win by a player to be a success, s.
a. Identify the success probability, p.
b. Construct a table showing the possible win-lose results and their probabilities for three games of craps. Round each probability to three decimal places.
c. Draw a tree diagram for part (b).
d. List the outcomes in which the player wins exactly two out of three times.
e. Determine the probability of each of the outcomes in part (d). Explain why those probabilities are equal.
f. Find the probability that the player wins exactly two out of three times.
g. Without using the binomial probability formula, obtain the probability distribution of the random variable Y, the number of times out of three that the player wins.
h. Identify the probability distribution in part (g). |
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| m102671 | The general addition rule for two events is presented in Formula 4.3 on page 175 and that for three events is displayed on page 177.
Formula 4.3
If A and B are any two events, then
P(A or B) = P(A) + P(B) − P(A & B).
P(A or B or C) = P(A) + P(B) + P(C) − P(A & B) − P(A & C) − P(B & C) + P(A & B & C).
a. Verify the general addition rule for three events.
b. Write the general addition rule for four events and explain your reasoning. |
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| m102672 | The Gini coefficient is a measure of the extent to which income or wealth is equally distributed in a given population. The coefficient values range between 0 and 1. The lower the Gini coefficient, the more equally distributed wealth is in a given population. The following figure represents the distribution of wealth based on this measure (reported at http://en.wikipedia.org/wiki/Gini_coefficient).
(a) What type of frequency distribution table is this?
(b) Is this an effective presentation of the data? Justify your answer. |
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| m102673 | The Head Injury Criterion (HIC) is a measure of the likelihood of an injury arising from an accident such as a vehicle crash. At an HIC of 1000, one in six people will suffer a life-threatening injury to the brain. The Insurance Institute for Highway Safety performs safety rating tests on vehicles. One of the variables measured is the HIC. The following data provide the HIC levels for a sample of small SUVs.
Use the technology of your choice to decide whether applying the Wilcoxon signed-rank test is reasonable. Explain your answers. |
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| m102674 | The Higher Education Research Institute of the University of California, Los Angeles, publishes information on characteristics of incoming college freshmen in The American Freshman. In 2000, 27.7% of incoming freshmen characterized their political views as liberal, 51.9% as moderate, and 20.4% as conservative. For this year, a random sample of 500 incoming college freshmen yielded the following frequency distribution for political views.
Political view Frequency
Liberal ................. 147
Moderate .............. 237
Conservative ......... 116
a. Determine the mode of the data.
b. Decide whether it would be appropriate to use either the mean or the median as a measure of center. Explain your answer. |
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| m102675 | The Higher Education Research Institute of the University of California, Los Angeles, publishes information on characteristics of incoming college freshmen in The American Freshman. In 2000, 27.7% of incoming freshmen characterized their political views as liberal, 51.9% as moderate, and 20.4% as conservative. For this year, a random sample of 500 incoming college freshmen yielded the following frequency distribution for political views.
Political view Frequency
Liberal....................................147
Moderate.................................237
Conservative.............................116
a. Identify the population and variable under consideration here.
b. At the 5% significance level, do the data provide sufficient evidence to conclude that this year s distribution of political views for incoming college freshmen has changed from the 2000 distribution?
c. Repeat part (b), using a significance level of 10%. |
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| m102676 | The highest dunes at Great Sand Dunes National Monument can exceed the highest dunes in the Great Sahara, extending over 700 feet in height. However, like all sand dunes, they tend to move around in the wind. This can cause a bit of trouble for temporary structures located near the "escaping" dunes. Roads, parking lots, campgrounds, small buildings, trees, and other vegetation are destroyed when a sand dune moves in and takes over. Such dunes are called "escape dunes" in the sense that they move out of the main body of sand dunes and, by the force of nature (prevailing winds), take over whatever space they choose to occupy. In most cases, dune movement does not occur quickly. An escape dune can take years to relocate itself. Just how fast does an escape dune move? Let x be a random variable representing movement (in feet per year) of such sand dunes (measured from the crest of the dune). Let us assume that x has a normal distribution with ( = 17 feet per year and ( = 3.3 feet per year. (For more information, see Hydrologic, Geologic, and Biologic Research at Great Sand Dunes National Monument and Vicinity, Colorado, proceedings of the National Park Service Research Symposium.)
Under the influence of prevailing wind patterns, what is the probability that
(a) An escape dune will move a total distance of more than 90 feet in 5 years?
(b) An escape dune will move a total distance of less than 80 feet in 5 years?
(c) An escape dune will move a total distance of between 80 |
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| m102677 | The highway department is testing two types of reflecting paint for concrete bridge end pillars. The two kinds of paint are alike in every respect except that one is orange and the other is yellow. The orange paint is applied to 12 bridges, and the yellow paint is applied to 12 bridges. After a period of 1 year, reflectometer readings were made on all these bridge end pillars. (A higher reading means better visibility.) For the orange paint, the mean reflectometer reading was x̅1 = 9.4, with standard deviation s1 = 2.1.
For the yellow paint, the mean was x̅2 = 6.9, with standard deviation s2 = 2.0.
Based on these data, can we conclude that the yellow paint has less visibility after 1 year? (Use a 1% level of signi ficance.)
(a) What is the level of signifi cance? State the null and alternate hypotheses.
(b) What sampling distribution will you use? What assumptions are you making? Compute the sample test statistic and corresponding distribution value.
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically signifi cant at level a?
(e) Interpret your conclusion in the context of the application.
For degrees of freedom d.f. not in the Student s t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and |
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| m102678 | The Honolulu Advertiser stated that in Honolulu there was an average of 661 burglaries per 100,000 households in a given year. In the Kohola Drive neighborhood there are 316 homes. Let r = number of these homes that will be burglarized in a year.
(a) Explain why the Poisson approximation to the binomial would be a good choice for the random variable r. What is n? What is p? What is l to the nearest tenth?
(b) What is the probability that there will be no burglaries this year in the Kohola Drive neighborhood?
(c) What is the probability that there will be no more than one burglary in the Kohola Drive neighborhood?
(d) What is the probability that there will be two or more burglaries in the Kohola Drive neighborhood? |
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| m102679 | The Internal Revenue Service compiles data on income tax returns and summarizes its findings in Statistics of Income. The first two columns of Table 4.16 show a frequency distribution (number of returns) for adjusted gross income (AGI) from federal individual income tax returns, where K = thousand.
A federal individual income tax return is selected at random.
a. Determine P(A), the probability that the return selected shows an AGI under $10K.
b. Find the probability that the return selected shows an AGI between $30K and $100K (i.e., at least $30K but less than $100K).
c. Compute the probability of each of the seven events in the third column of Table 4.16, and record those probabilities in the fourth column. |
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| m102680 | The Internal Revenue Service (IRS) decides that it will audit the returns of 3 people from a group of 18. Use combination notation to express the number of possibilities and then evaluate that expression. |
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| m102681 | The January mean number of sunspots is recorded for a sequence of recent Januaries.
Use level of signifi cance 5% to test for randomness about the median. Interpret the results. |
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| m102682 | The Japan Automobile Manufacturer s Association provides data on exported vehicles in Motor Vehicle Statistics of Japan. In 2010, cars, trucks, and buses constituted 88.3%, 9.3%, and 2.4%of vehicle exports, respectively. A random sample of last year s exports yielded the vehicle-type data on the WeissStats site.
a. Determine a frequency distribution.
b. Obtain a relative-frequency distribution.
c. Draw a pie chart.
d. Construct a bar chart.
If an exercise discusses more than one data set, do parts (a)-(d) for each data set. |
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| m102683 | The Japan Automobile Manufacturers Association provides data on exported vehicles in Motor Vehicle Statistics of Japan. In 2010, cars, trucks, and buses constituted 88.3%, 9.3%, and 2.4% of vehicle exports, respectively. A random sample of last year s exports yielded the vehicle-type data on the WeissStats site.
Use the technology of your choice to obtain the measures of center that are appropriate from among the mean, median, and mode. Discuss your results and decide which measure of center is most appropriate. Provide a reason for your answer. |
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| m102684 | The job-order cost sheet is a subsidiary account to
a. Raw Materials.
b. Work in Process.
c. Finished Goods.
d. Cost of Goods Sold.
e. Jobs Started. |
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| m102685 | The loss, in millions of dollars, due to a fire in a commercial building is a variable with density curve y = 1 − x/2 for 0 < x < 2, and y = 0 otherwise. Using the fact that the area of a triangle equals one-half its base times its height, we find that the area under this density curve to the left of any number x between 0 and 2 equals x − x2/4.
a. Graph the density curve of this variable.
b. What percentage of losses exceed $1.5 million? |
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| m102686 | The majority party of the U.S. House of Representatives for each year from 1973 to 2003 follow, where D and R represent Democrat and Republican, respectively
D D D D D D D D D D D R R R R R R R
Test the sequence for randomness. Use a = 0.05.
(a) What is the level of signifi cance? State the null and alternate hypotheses.
(b) Find the sample test statistic R, the number of runs.
(c) Find the upper and lower critical values in Table 10 of Appendix II.
(d) Conclude the test.
(e) Interpret the conclusion in the context of the application. |
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| m102687 | The manager of Motel 11 has 316 rooms in Palo Alto, California. From observation over a long period of time, she knows that on an average night, 268 rooms will be rented. The long-term standard deviation is 12 rooms. This distribution is approximately mound-shaped and symmetric.
(a) For 10 consecutive nights, the following numbers of rooms were rented each night:
Make a control chart for the number of rooms rented each night, and plot the preceding data on the control chart. Interpretation Looking at the control chart, would you say the number of rooms rented during this 10-night period has been unusually low? unusually high? about what you expected? Explain your answer. Identify all out-of-control signals by type (I, II, or III).
(b) For another 10 consecutive nights, the following numbers of rooms were rented each night:
Make a control chart for the number of rooms rented each night, and plot the preceding data on the control chart. Interpretation Would you say the room occupancy has been high? low? about what you expected? Explain your answer. Identify all out-of-control signals by type (I, II, or III)? |
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| m102688 | The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotel s accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of future weekend guest bills to test the manager s claim.
a. Which form of the hypotheses should be used to test the manager s claim? Explain.
b. What conclusion is appropriate when H0 cannot be rejected?
c. What conclusion is appropriate when H0 can be rejected? |
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| m102689 | The margin of error is also called the maximum error of the estimate. Explain why. |
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