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m1  Twenty percent of a particular age group has hypertension. Five percent of this age group has hypertension and diabetes. Given that an individual from this age group has hypertension, what is the probability that the individual also has diabetes? 

m10  1. Develop a graph or table that portrays the checking balances. What is the balance of a typical customer? Do many customers have more than $2,000 in their accounts? Does it appear that there is a difference in the distribution of the accounts among the four branches?
Around what value do the account balances tend to cluster?
2. Determine the mean and median of the checking account balances. Compare the mean and the median balances for the four branches. Is there a difference among the branches? Be sure to explain the difference between the mean and the median in your report.
3. Determine the range and the standard deviation of the checking account balances. What do the first and third quartiles show? Determine the coefficient of skewness and indicate what it shows. Because Mr. Selig does not deal with statistics daily, include a brief description and interpretation of the standard deviation and other measures.
Century National Bank has offices in several cities in the Midwest and the southeastern part of the United States. Mr. Dan Selig, president and CEO, would like to know the characteristics of his checking account customers. What is the balance of a typical customer? How many other bank services do the checking account customers use? Do the customers use the ATM service and, if so, how often? What about debit cards? Who uses them, and how often are they used? 

m11  1. Let f, g: A >R be integrable.
a. For any partition of and any subrectangle of , show that and and therefore and . 
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m13  14. If is a closed rectangle, show that is Jordan measurable if and only if for every there is a partition of such that , where consists of all subrectangles intersecting and consists of allsubrectangles contained in . 

m27  A bicycle manufacturer randomly selects 10 frames each day and tests for defects. The numbers of defective frames found over the last 14 days are 3, 2, 1, 3, 2, 2, 8, 2, 0, 3, 5, 2, 0, and 4. Construct a control chart for this process and comment on whether the process is “in control.” 
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m28  A Buffalo, New York, cola distributor is featuring a superspecial sale on 12packs. She wonders where in the grocery store to place the cola for maximum attention. Should it be near the front door of the grocery stores, in the cola section, at the checkout registers, or near the milk and other dairy products? Four stores with similar total sales cooperated in an experiment. In one store, the 12packs were stacked near the front door, in another they were placed near the checkout registers, and so on. Sales were checked at specified times in each store for exactly four minutes. The results were:
...The Buffalo distributor wants to find out whether there is a difference in the mean sales for cola stacked at the four locations in the store. Use the .05 significance level.
(a) The null and the alternate hypotheses,
(b) The decision rule, and
(c) The decision regarding the null hypothesis,
(d) Then interpret theresult. 
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m29  A candy company taste tested two chocolate bars, one with almonds and one without almonds. A panel of testers rated the bars on a scale of 0 to 5, with 5 indicating the highest taste rating. If the bar had almonds, the rating was assigned a code of 1; if the bar did not have almonds, the rating was assigned a code of 0. Assume the population standard deviations are equal. At the .05 significance level, do the ratings show a difference between chocolate bars with or withoutalmonds? 

m30  A carbon monoxide detector in the Wheelock household activates once every 200 days on average. Assume this activation follows the exponential distribution. What is the probability that:
a. There will be an alarm within the next 60 days?
b. At least 400 days will pass before the next alarm?
c. It will be between 150 and 250 days until the next warning?
d. Find the median time until the next activation. 
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m31  A case of 24 cans contains 1 can that is contaminated. Three cans are to be chosen randomly for testing.
a. How many different combinations of three cans could be selected?
b. What is the probability that the contaminated can is selected for testing? 

m32  A cell phone company offers two plans to its subscribers. At the time new subscribers sign up, they are asked to provide some demographic information. The mean yearly income for a sample of 40 subscribers to Plan A is $57,000 with a standard deviation of $9,200. For a sample of 30 subscribers to Plan B, the mean income is $61,000 with a standard deviation of $7,100. At the .05 significance level, is it reasonable to conclude the mean income of those selecting Plan B is larger? What is the pvalue? 

m33  A chain of sport shops catering to beginning skiers, headquartered in Aspen, Colorado, plans to conduct a study of how much a beginning skier spends on his or her initial purchase of equipment and supplies. Based on these figures, it wants to explore the possibility of offering combinations, such as a pair of boots and a pair of skis, to induce customers to buy more. A sample of 44 cash register receipts revealed these initial purchases:..
a. Arrive at a suggested class interval.
b. Organize the data into a frequency distribution using a lower limit of $70.
c. Interpret yourfindings. 
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m34  A coffee manufacturer is interested in whether the mean daily consumption of regular coffee drinkers is less than that of decaffeinatedcoffee drinkers. Assume the population standard deviation for those drinking regular coffee is 1.20 cups per day and 1.36 cups per day for those drinking decaffeinated coffee. A random sample of 50 regularcoffee drinkers showed a mean of 4.35 cups per day. A sample of 40 decaffeinatedcoffee drinkers showed a mean of 5.84 cups per day. Use the .01 significance level. Compute the pvalue. 
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m35  A coin toss is used to decide which team gets the ball first in most sports. It involves little effort and is believed to give each side the same chance. In 47 Super Bowl games, the National Football Conference has won the coin flip 31 times. Meanwhile, the American Football Conference has won only 16 times. Use the sixstep hypothesistesting procedure at the .01 significance level to test whether these data suggest a fair coin flip.
a. Why can you employ Z as the test statistic?
b. State the null and alternate hypotheses.
c. Make a diagram of the decision rule.
d. Evaluate the test statistic and make the decision.
e. What is the pvalue and what does that imply? 

m36  A coladispensing machine is set to dispense 9.00 ounces of cola per cup, with a standard deviation of 1.00 ounce. The manufacturer of the machine would like to set the control limit in such a way that, for samples of 36, 5% of the sample means will be greater than the upper control limit, and 5% of the sample means will be less than the lower control limit.
a. At what value should the control limit be set?
b. If the population mean shifts to 8.6, what is the probability of detecting the change?
c. If the population mean shifts to 9.6, what is the probability of detecting the change? 

m37  a. Compute the mean of the following sample values: 1.3, 7.0, 3.6, 4.1, 5.0.
b. Show that o(x 2 x) 5 0. 

m38  a. Compute the mean of the following sample values: 5, 9, 4, 10.
b. Show that o(x 2 x ) 5 0. 

m39  A computer manufacturer offers a help line that purchasers can call for help 24 hours a day, 7 days a week. Clearing these calls for help in a timely fashion is important to the company’s image. After telling the caller that resolution of the problem is important, the caller is asked whether the issue is software or hardware related. The mean time it takes a technician to resolve a software issue is 18 minutes with a standard deviation of 4.2 minutes. This information was obtained from a sample of 35 monitored calls. For a study of 45 hardware issues, the mean time for the technician to resolve the problem was 15.5 minutes with a standard deviation of 3.9 minutes. This information was also obtained from monitored calls. At the .05 significance level, does it take longer to resolve software issues? What is the pvalue? 
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m40  A computersupply retailer purchased a batch of 1,000 CDR disks and attempted to format them for a particular application. There were 857 perfect CDs, 112 CDs were usable but had bad sectors, and the remainder could not be used at all.
a. What is the probability a randomly chosen CD is not perfect?
b. If the disk is not perfect, what is the probability it cannot be used at all? 
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m41  A consulting group was hired by the Human Resources Department at General Mills, Inc. to survey company employees regarding their degree of satisfaction with their quality of life. A special index, called the index of satisfaction, was used to measure satisfaction. Six factors were studied, namely, age at the time of first marriage (x1), annual income (x2), number of children living (x3), value of all assets (x4), status of health in the form of an index (x5), and the average number of social activities per week—such as bowling and dancing (x6).
Suppose the multiple regression equation is:
yˆ = 16.24 + 0.017x1 + 0.0028 x2 + 42x3 + 0.0012x4 + 0.19x5 + 26.8x6
a. What is the estimated index of satisfaction for a person who first married at 18, has an annual income of $26,500, has three children living, has assets of $156,000, has an index of health status of 141, and has 2.5 social activities a week on the average?
b. Which would add more to satisfaction, an additional income of $10,000 a year or two more social activities a week? 
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m42  A consumer analyst collected the following data on the screen sizes of popular LCD televisions sold recently at a large retailer:..
a. Does there appear to be a linear relationship between the screen size and the price?
b. Which variable is the “dependent” variable?
c. Using statistical software, determine the regression equation. Interpret the value of the slope in the regression equation.
d. Include the manufacturer in a multiple linear regression analysis using a “dummy” variable. Does it appear that some manufacturers can command a premium price?
e. Test each of the individual coefficients to see if they are significant.
f. Make a plot of the residuals and comment on whether they appear to follow a normal distribution.
g. Plot the residuals versus the fitted values. Do they seem to have the same amount ofvariation? 
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