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introduction to business statistics

Introduction To Probability And Statistics 13th Edition William Mendenhall, Robert J. Beaver, Barbara M. Beaver - Solutions

Repeat Exercise 6.1. Use Table 3 and fill in the probabilities below. Write the Rewrite the Probability (if needed) Find the Probability The Interval Probability Greater than 5 Between -3 and 3 Between -.5 and 1.5 Less than or equal to –6.7 Less than 2.81 P(z> PL PL
Use the applet to find the following:a. P(x < 6) for n = 22, p = .65b. P(x = 8) for n = 12, p = .4c. P(x > 14) for n = 20, p = .5d. P(2 < x < 6) for n = 15, p = .3e. P(x ≥ 6) for n = 50, p = .7
Many employers provide workers with sick/personal days as well as vacation days. Among workers who have taken a sick day when they were not sick, 49% say that they needed a break! Suppose that a random sample of n = 12 workers who took a sick day is selected. Rounding 49% to p = .5, find the
A manufacturer of videotapes ships them in lots of 1200 tapes per lot. Before shipment, 20 tapes are randomly selected from each lot and tested. If none is defective, the lot is shipped. If one or more are defective, every tape in the lot is tested.a. What is the probability distribution for x, the
Although teen magazines Teen People, Hachette Filipacche, and Elle Girl folded in 2006, 70% of people in a phone-in poll said teens are still a viable market for print, but they do not want titles that talk to them like they are teens. They read more sophisticated magazines. A sample of n = 400
A USA Today Snapshot reports that among people 35 to 65 years old, nearly two thirds say they are not concerned about being forced into retirement. Suppose that we randomly select n = 15 individuals that in this age category and approximate the value of p as p = .7. Let x be the number that say
The table below shows the prices of 8 single handset cordless phones along with their overall score (on a scale of 0€“100) in a consumer rating survey presented by Consumer Reports.a. Calculate the correlation coefficient r between price and overall score. How would you describe the
Acess the applet called Exploring Correlation.a. Move the slider in the first applet so that r ≈ .75. Now switch the sign using the button at the bottom of the applet. Describe the change in the pattern of the points.b. Move the slider in the first applet so that r ≈ 0. Describe the pattern of
Access the applet in How a Line Works.a. Use the slider to change the y-intercept of the line, but do not change the slope. Describe the changes that you see in the line.b. Use the slider to change the slope of the line, but do not change the y-intercept. Describe the changes that you see in the
Use event relationships to fill in the blanks in the table below. PLA U B)| P(A|B) Conditions for Events A and PIAN B) P(B) PLA) 3 .12 .3 .7 Mutually exclusive .5 .1 Independent .5 2.
Use event relationships to fill in the blanks in the table below. Conditions for Events A and B P(AN B) P(AU B) P(A) .3 P(B) 4 4 4 P(AB) Mutually exclusive Independent .3 .1 .2 .5 .1 .5
The two stars of the Miami Heat professional basketball team are very different when it comes to making free throws. ESPN.com reports that Jason Williams makes about 80% of his free throws, while Shaquille O’Neal makes only 53% of his free throws.4 Assume that the free throws are independent, and
Who is the king of late night TV? An Internet survey estimates that, when given a choice between David Letterman and Jay Leno, 52% of the population prefers to watch Jay Leno. Suppose that you randomly select three late night TV watchers and ask them which of the two talk show hosts they prefer.a.
Two tennis professionals, A and B, are scheduled to play a match; the winner is the first player to win three sets in a total that cannot exceed five sets. The event that A wins any one set is independent of the event that A wins any other, and the probability that A wins any one set is equal to
“Whistle blowers” is the name given to employees who report corporate fraud, theft, or other unethical and perhaps criminal activities by fellow employees or by their employer. Although there is legal protection for whistle blowers, it has been reported that approximately 23% of those who
A fire-detection device uses three temperature-sensitive cells acting independently of one another in such a manner that any one or more can activate the alarm. Each cell has a probability p = .8 of activating the alarm when the temperature reaches 100°F or higher. Let x equal the number of cells
Is your chance of getting a cold influenced by the number of social contacts you have? A study by Sheldon Cohen, a psychology professor at Carnegie Mellon University, seems to show that the more social relationships you have, the less susceptible you are to colds. A group of 276 healthy men and
The number of companies offering flexible work schedules has increased as companies try to help employees cope with the demands of home and work. One flextime schedule is to work four 10-hour shifts. However, a big obstacle to flextime schedules for workers paid hourly is state legislation on
Access the Flipping Fair Coins applet. The experiment consists of tossing three fair coins and recording x, the number of heads.a. Use the laws of probability to write down the simple events in this experiment.b. Find the probability distribution for x. Display the distribution in a table and in a
Refer to Exercise 4.138.a. If you were to toss only one coin, what would the probability distribution for x look like?b. Perform a simulation using the Flipping Fair Coins applet with n = 1, and compare your results with part a.
Refer to Exercise 4.138. Access the Flipping Weighted Coins applet. The experiment consists of tossing three coins that are not fair, and recording x, the number of heads.a. Perform a simulation of the experiment using the Flipping Weighted Coins applet. Is the distribution symmetric or skewed?
Consider a binomial random variable with n = 8 and p = .7. Isolate the appropriate column in Table 1 and fill in the probabilities below.Fill in the blanks in the table below. 4 3 2 5 P(x< k) List the Values of x Probability Write the Rewrite the Find the Probability The Problem 3 or less 3 or
Consider a binomial random variable with n = 9 and p = .3. Isolate the appropriate column in Table 1 and fill in the probabilities below.Fill in the blanks in the table below. 0 1 2 3 4 5 6 7 8 9 P(xs k) List the Write the Rewrite the Probability Probability Find the Probability The Problem Values
A jar contains five balls: three red and two white. Two balls are randomly selected without replacement from the jar, and the number x of red balls is recorded. Explain why x is or is not a binomial random variable. If the experiment is binomial, give the values of n and p.
P(x ≤ k) in each case:a. n = 20, p = .05, k = 2b. n = 15, p = .7, k = 8c. n = 10, p = .9, k = 9
Let x be a binomial random variable with n = 20 and p = .1.a. Calculate P(x ‰¤ 4) using the binomial formula.b. Calculate P(x ‰¤ 4) using Table 1 in Appendix I.c. Use the MINITAB output at the top of the page to calculate P(x ‰¤ 4). Compare the results of parts
In 2006, the average combined SAT score (reading + verbal + writing) for college-bound students in the United States was 1518 (out of 2400). Suppose that approximately 45% of all high school graduates took this test, and that 100 high school graduates are randomly selected from throughout the
Of all the Harry Potter books purchased in a recent year, about 60% were purchased for readers 14 or older. If 12 Harry Potter fans who bought books that year are surveyed and if p = .6, find the following probabilities.a. At least five of them are 14 or older.b. Exactly nine of them are 14 or
Consider a Poisson random variable with Î¼ = 2.5. Calculate the following probabilities using the following table. Calculated Value Probability Formula P(x = 0) k! P(x = 1) k! P(x = 2) k! P(2 or fewer successes) ) + P(x=) + P(x=_ P(x =
Consider a Poisson random variable with Î¼ = 3. Calculate the following probabilities using the table below. Calculated Value Formula Probability P(x = 0) k! P(x = 1) k! P(more than 1 success) 1- [P(x = + P(x = ]
Consider a Poisson random variable with Î¼ = 3. Isolate the appropriate column in Table 2 and fill in the probabilities below.Fill in the blanks in the table below. 4 1 3 5 10 P(xs k) List the Write the Values of x Probability P(xs) Rewrite the Probability (if needed) Find the The
Consider a Poisson random variable with Î¼ = 0.8. Isolate the appropriate column in Table 2 and fill in the probabilities below.Fill in the blanks in the table below. 1 2 3 4 P(x < k) List the Values of x Probability Rewrite the Probability (if needed) Write the Find the The Problem
Increased research and discussion have focused on the number of illnesses involving the organism Escherichia coli (01257:H7), which causes a breakdown of red blood cells and intestinal hemorrhages in its victims. According to the Center for Disease Control, an estimated 73,000 cases of E. coli
Repeat the instructions in Exercise 7.85 when three dice are tossed.Two balanced dice are thrown, and the average number on the two upper faces is recorded.a. Use the values μ = 3.5 and σ = 1.71 from Exercise 7.84. What are the theoretical mean and standard deviation of the sampling distribution
Two balanced dice are thrown, and the average number on the two upper faces is recorded.a. Use the values μ = 3.5 and σ = 1.71 from Exercise 7.84. What are the theoretical mean and standard deviation of the sampling distribution for x?b. Use the Central Limit Theorem applet to toss a single die
Refer to the die-tossing experiment with n = 1 in Section 7.4 in which x is the number on the upper face of a single balanced die.a. Use the formulas in Section 4.8 to verify that μ = 3.5 and σ = 1.71 for this population.b. Use the Central Limit Theorem applet to toss a single die at least 2000
During long production runs of canned tomatoes, the average weights (in ounces) of samples of five cans of standard- grade tomatoes in pureed form were taken at 30 control points during an 11-day period. These results are shown in the table. When the machine is performing normally, the average
Refer to Exercise 7.75. During a given week the number of defective bulbs in each of five samples of 100 were found to be 2, 4, 9, 7, and 11. Is there reason to believe that the production process has been producing an excessive proportion of defectives at any time during the week?
The results of a Newsweek poll concerning views on abortion given in the table that follows show that there is no consensus on this issue among Americans.Newsweek Poll conducted by Princeton Survey Research Associates International. Oct. 26€“27, 2006. N = 1002 adults nationwide. MoE
Refer to Exercise 7.58 and suppose that during a day when the state of the 32-ounce bat production process was unknown, the following measurements were obtained at hourly intervals.Each measurement represents a statistic computed from a sample of five bat weights selected from the production
A gambling casino records and plots the mean daily gain or loss from five blackjack tables on an x̅ chart. The overall mean of the sample means and the standard deviation of the combined data over 40 weeks were x̅̅ = $10,752 and s = $1605, respectively.a. Construct an x̅ chart for the mean
The sample means were calculated for 40 samples of size n = 5 for a process that was judged to be in control. The means of the 40 values and the standard deviation of the combined 200 measurements were x̅ = 155.9 and s = 4.3, respectively.a. Use the data to determine the upper and lower control
The sample means were calculated for 30 samples of size n = 10 for a process that was judged to be in control. The means of the 30 x̅-values and the standard deviation of the combined 300 measurements were x̅ = 20.74 and s = .87, respectively.a. Use the data to determine the upper and lower
In the spring of 2004, the U.S. Congress considered a bill that would prevent Americans from suing fast-food giants like McDonald’s for making them overweight. Although the fast-food industry may not be to blame, a study by Children’s Hospital in Boston reports that about two thirds of adult
The cost of brand-name prescriptions are set to provide support for research and development of these drugs, which may cover as many as 20 years. Nonetheless, a majority of Americans say that costs of prescription drugs (66%), hospital costs (64%), and doctors visits (55%) are unreasonably high.
News reports tell us that the average American is overweight. Many of us have tried to trim down to our weight when we finished high school or college. And, in fact, only 19% of adults say they do not suffer from weight-loss woes. Suppose that the 19% figure is correct, and that a random sample of
To find the probability that the sample proportion is less than .8, write down the event of interest ________.When pÌ‚ = .8,Find the probability:P(pÌ‚ < ________) = P(z < ________) = ________ pq У п
You take a random sample of size n = 50 from a binomial distribution with a mean of p = .7. The sampling distribution of p̂ will be approximately _________ with a mean of _________ and a standard deviation (or standard error) of _________.
Refer to Exercise 7.15. To find the probability that the sample mean is greater than 55, write down the event of interest ______. When xÌ… = 55,Find the probability:P(xÌ… > _______) = P(z > _______) = 1 - _______ = _______ -μ μ σνη || ||
You take a random sample of size n = 49 from a distribution with mean μ = 53 and σ = 21. The sampling distribution of x̅ will be approximately ______ with a mean of ______ and a standard deviation (or standard error) of ______.
Two different Gallup Polls were conducted for CNN/USA Today, both of which involved people€™s feelings about the U.S. space program. Here is a question from each poll, along with the responses of the sampled Americans:
A study of an experimental blood thinner was conducted to determine whether it works better than the simple aspirin tablet in warding off heart attacks and strokes. The study, reported in the Press Enterprise, involved 19,185 people who had suffered heart attacks, strokes, or pain from clogged
In many states, lists of possible jurors are assembled from voter registration lists and Department of Motor Vehicles records of licensed drivers and car owners. In what ways might this list not cover certain sectors of the population adequately?
A random sample of public opinion in a small town was obtained by selecting every 10th person who passed by the busiest corner in the downtown area. Will this sample have the characteristics of a random sample selected from the town’s citizens? Explain.
A small city contains 20,000 voters. Use the random number table to identify the voters to be included in a random sample of n = 15.
A population contains 50,000 voters. Use the random number table to identify the voters to be included in a random sample of n = 15.
Although faculty salaries at colleges and universities in the United States continue to rise, they do not always keep pace with the cost of living nor with salaries in the private sector. In 2005, the National Center for Educational Statistics indicated that the average salary for Assistant
Refer to Exercise 6.83. For ease of calculation, round the number of standard deviations for “C” grades to ± .5 standard deviations, and for “B” and “D” grades to ± 1.5 standard deviations. Suppose that the distribution of grades for a large class of students has an average of 78 with
Find the probability that z lies between z = - 1.48 and z = 1.48.
a. Find the probability that z is greater than - .75.b. Find the probability that z is less than 1.35.
How often do you watch movies at home? A USA Today Snapshot found that about 7 in 10 adults say they watch movies at home at least once a week. Suppose a random sample of n = 50 adults are polled and asked if they had watched a movie at home this week. Let us assume that p = .7 is, in fact,
Fill in the blanks in the table below and find the necessary sample sizes. One or Two Samples Margin of Error Type of Data Bound, Solve This Inequality Sample Size
Fill in the blanks in the table below and find the necessary sample sizes. One or Two Samples Type of Data Bound, Solve This B Margin of Error Sample Size Inequality p or o Binomial
The voters in the midterm 2006 elections showed that Democrat and Republican differences extend beyond matters of opinion, and actually include the way they see the world. The three most important issues mentioned by Democrats and Republicans are listed below.Use a large-sample estimation procedure
Refer to Exercise 8.18. The means and standard deviations for 50 billing statements from each of the computer databases of each of the three hotel chains are given in the table:a. Find a 95% confidence interval for the difference in the average room rates for the Marriott and the Wyndham hotel
College graduates are getting more for their degrees as starting salaries rise. To compare the starting salaries of college graduates majoring in chemical engineering and computer science, random samples of 50 recent college graduates in each major were selected and the following information
How likely are you to vote in the next presidential election? A random sample of 300 adults was taken, and 192 of them said that they always vote in presidential elections.a. Construct a 95% confidence interval for the proportion of adult Americans who say they always vote in presidential
Women on Wall Street can earn large salaries, but may need to make sacrifices in their personal lives. In fact, many women in the securities industry have to make significant personal sacrifices. A survey of 482 women and 356 men found that only half of the women have children, compared to
The average American has become accustomed to eating away from home, especially at fast-food restaurants. Partly as a result of this fast-food habit, the per-capita consumption of cheese (the main ingredient in pizza) and nondiet soft drinks has risen dramatically from a decade ago. A study in
Don’t Americans know that eating pizza and french fries leads to being overweight? In the same American Demographics article referenced in Exercise 8.98, a survey of women who are the main meal preparers in their households reported these results:• 90% know that obesity causes health
For a number of years, nearly all Americans say that they would vote for a woman for president IF she were qualified, and IF she were from their own political party. But is America ready for a female president? A CBS/New York Times poll asked this question of a random sample of 1229 adults, with
A dean of men wishes to estimate the average cost of the freshman year at a particular college correct to within $500, with a probability of .95. If a random sample of freshmen is to be selected and each asked to keep financial data, how many must be included in the sample? Assume that the dean
In addition to teachers and administrative staff, schools also have many other employees, including bus drivers, custodians, and cafeteria workers. The average hourly wage is $14.18 for bus drivers, $12.61 for custodians, and $10.33 for cafeteria workers. Suppose that a school district employs n =
Refer to the Interpreting Confidence Intervals applet.a. Suppose that you have a random sample of size n = 50 from a population with unknown mean μ and known standard deviation σ = 35. Calculate the half width of a 95% confidence interval for μ. What would the width of this interval be?b. Use
You have a coin that you think is fair, with π = probability of heads = 1/2. To check, you plan to flip the coin n times.a. Compute the SD of p̂ for each value of n in the table below and fill in your SD values.n ...............................SD of p̂1020401005001,000b. Plot SD(p̂) on the
It has been reported that the median price of a home purchased in Portland, Oregon, during 2001 was $172,300. For a random sample of homes purchased in a certain area of the city during that year, the prices were as listed below. Using the 0.025 level of significance, test whether the median
In previous chapters, confidence intervals have been expressed in terms of a sample statistic plus or minus a given expression x̅ + t(s/√n). However, the confidence interval for σ2 cannot be expressed as s2 plus or minus a comparable term. Why is this not possible?
In applying the chi-square statistic to estimation and tests for a population variance, why must the population be normally distributed?
Reconsider the previous exercise about sex and coff ee consumption. The sample data could be organized in a two-way table as follows:a. Fill in the table with counts (which you make up) in such a way that there€™s almost no association between sex and coffee consumption. Also draw the
The monthly utility bills for a household in Riverside, California, were recorded for 12 consecutive months starting in January 2006:a. Construct a box plot for the monthly utility costs. b. What does the box plot tell you about the distribution of utility costs for this household? Amount ($)
If you scored at the 69th percentile on a placement test, how does your score compare with others?
Find the five-number summary and the IQR for these data:19, 12, 16, 0, 14, 9, 6, 1, 12, 13, 10, 19, 7, 5, 8
Below you will find three data sets that have already been sorted. Fill in the blanks to find the upper and lower quartiles. Measurements Above and Below and Measurements Above and Below and Position of Q3 Sorted Data Set Position of Q1 1, 1.5, 2, 2, 2.2 0, 1.7, 1.8, 3.1, 3.2, 7,8, 8.8, 8.9, 9, 10
Below you will find two practice data sets. Fill in the blanks to find the necessary quartiles. Lower Upper Sorted Position of Q4 Position of Q3 Quartile, Q Quartile, Q3 Data Set .13, .76, .34, .88, .21, .16, .28 2.3, 1.0, 2.1, 6.5, 2.8, 8.8, 1.7, 2.9, 4.4, 5.1, 2.0
The number of passes completed by Brett Favre, quarterback for the Green Bay Packers, was recorded for each of the 16 regular season games in the fall of 2006 (www.espn.com).a. Draw a stem and leaf plot to describe the data.b. Calculate the mean and standard deviation for Brett Favre€™s
The data from Exercise 1.70 (see data set EX0170), reproduced below, show the last digit of the Social Security number for a group of 70 students.a. You found in Exercise 1.70 that the distribution of this data was relatively €œflat,€ with each different value from 0 to 9
The monthly utility bills for a household in Riverside, California, were recorded for 12 consecutive months starting in January 2006:a. Calculate the range of the utility bills for the year 2006.b. Calculate the average monthly utility bill for the year 2006.c. Calculate the standard deviation for
The cost of televisions exhibits huge variation—from $100–200 for a standard TV to $8,000–10,000 for a large plasma screen TV. Consumer Reports gives the prices for the top 10 LCD high definition TVs (HDTVs) in the 30- to 40-inch category:6Brand
The number of Starbucks coffee shops in 18 cities within 20 miles of the University of California, Riverside is shown in the following table (www.starbucks.com).a. Find the mean, the median, and the mode.b. Compare the median and the mean. What can you say about the shape of this distribution?c.
The cost of automobile insurance has become a sore subject in California because insurance rates are dependent on so many different variables, such as the city in which you live, the number of cars you insure, and the company with which you are insured. The website www.insurance.ca.gov reports
Ten of the 50 largest businesses in the United States, randomly selected from the Fortune 500, are listed below along with their revenues (in millions of dollars):2a. Draw a stem and leaf plot for the data. Are the data skewed?b. Calculate the mean revenue for these 10 businesses. Calculate the
The following data set records the yearly charitable contributions (in dollars) to the United Fund for a group of employees at a public university.Use the second applet in Building a Histogram to construct a relative frequency histogram for the data. What is the shape of the distribution? Can you
The number of Starbucks coffee shops in cities within 20 miles of the University of California, Riverside is shown in the following table.a. Draw a dotplot to describe the data.b. Describe the shape of the distribution.c. Is there another variable that you could measure that might help to explain
The most popular colors for compact and sports cars in a recent year are given in the table.5Use an appropriate graphical display to describe these data. Percentage 20 Percentage Color Color Silver Gray Blue Black White Red Green Light Brown Yellow/Gold Other 17 16 14 10 5 1 2
The following are the 2006 state gasoline tax rates in cents per gallon for the 50 United States and the District of Columbia.5a. Construct a stem and leaf display for the data.b. How would you describe the shape of this distribution?c. Are there states with unusually high or low gasoline taxes? If
An advertisement in a recent Time magazine claimed that Geico Insurance will help you save an average of $200 per year on your automobile insurance.15a. Construct a relative frequency histogram to describe the average savings for the 27 states shown on the United States map. Do you see any unusual
The mobile Internet is growing, with users accessing sites such as Yahoo! Mail, the Weather Channel, ESPN, Google, Hotmail, and Mapquest from their cell phones. The most popular web browsers are shown in the table below, along with the percentage market share for each.14a. Do the percentages add up
Many opinion polls have tracked opinions regarding the fear of terrorist attacks following the September 11, 2001, attacks on the World Trade Center. A Newsweek poll conducted by Princeton Survey Research Associates International presented the results of several polls over a two-year period that
Refer to Exercises 1.51 and 1.52. The accompanying stem and leaf plots were generated using MINITAB for the variables named €œPopular Vote€ and €œPercent Vote.€a. Describe the shapes of the two distributions. Are there any outliers?b. Do the stem and leaf
Education pays off, according to a snapshot provided in a report to the city of Riverside by the Riverside County Office of Education. 7 The average annual incomes for six different levels of education are shown in the table:

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