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introduction to probability statistics

Statistics Principles And Methods 6th Edition Richard A. Johnson - Solutions

Refer to Exercise 4.53. Let C denote the event that the employee gets either lunch or flowers or both.(a) Relate C to the events A and B, and calculate P(C) using a law of probability.(b) State the composition of C and calculate its probability by adding the probabilities of the simple events.
A person is randomly selected from persons working in your state. Consider the two eventsGiven that the person selected drives a new luxury car, would you expect the probability of A to be larger, the same, or smaller than the unconditional probability P(A)? Explain your answer. Are A and B
Refer to Exercise 4.45. Find(a) the conditional probability that A occurs given that B occurs.(b) the conditional probability that B occurs given that A does not occur.
Refer to Exercise 4.69. Now suppose 3 air conditioners will be selected at random and checked one after another. Find the probability that:(a) All 3 are good.(b) The first 2 are good and the third defective.(c) Two are good and 1 defective.
If a coin is tossed 11 times, the outcome can be recorded as an 11-character sequence of H’s and T’s according to the results of the successive tosses. In how many ways can there be 4 H’s and 7 T’s? (Put differently, in how many ways can one choose 4 positions out of 11 to put the letter H?)
Ordered sampling versus unordered sampling.Refer to Exercise 4.91. Suppose the sampling of 3 alternators is done by randomly choosing one after another and without replacement.The event A can then be described as G1G2G3 , where G denotes “good” and the suffixes refer to the order of the draws.
Nine agricultural plots for an experiment are laid out in a square grid as shown. Three plots are to be selected at random.(a) Find the probability that all 3 are in the same row.(b) Find the probability that all 3 are in different rows. 1 2 3 4 5 6 7 8 9
List all the samples from {a,b, c,d, e} when (a)2 out of 5 are selected, (b) 3 out of 5 are selected.Count the number of samples in each case.
Evaluate: (a) '6' 3, (b) (49) (c) 22 22 2 (d) 222 30 30 (e) (f) 20 3. 27,
Of three events, A, B, and C, suppose events A and B are independent and events B and C are mutually exclusive. Their probabilities are.7, and Express the following events in set notation and calculate their probabilities.(a) Both B and C occur.(b) At least one of A and B occurs.(c) B does not
An electronic scanner is successful in detecting flaws in a material in 80% of the cases. Three material specimens containing flaws will be tested with the scanner. Assume that the tests are independent.(a) List the sample space and assign probabilities to the simple events.(b) Find the probability
Consider tossing two fair coins and the events A: Head in the first toss B: Head in the second toss C: Both heads or both tails in the two tosses(a) Verify that the property of independence holds for all event pairs.(b) Show that is different from the product (This illustrates the fact that
Imperfect clinical test. Repeat Example 20 but change to .96.
The height that bread rises may be one indicator of how light it will be. As a first step, before modifying her existing recipe, a student cook measured the raise height (cm) on eight occasions:6.3 6.9 5.7 5.4 5.6 5.5 6.6 6.5 Find the mean and median of the raised heights.
The monthly income in dollars for seven sales persons at a car dealership are 2450 2275 2425 4700 2650 2350 2475(a) Calculate the mean and median salary.(b) Which of the two is preferable as a measure of center and why?
A major wine producer reported sales (in hundreds of cases) for two-week periods during one summer:85 82 77 83 80 77 94 Obtain the sample mean and median.
Recent crime reports on the number of aggravated assaults at each of the 27 largest universities reporting for the year are summarized in the computer output Descriptive Statistics: AggAslt Variable N Mean Median StDev AggAslt 27 10.30 10.00 7.61 Locate two measures of center tendency, or location,
Calculate the mean and median for each of the following data sets.(a) 2 5 1 4 3(b) 26 30 38 32 26 31(c) 1 2 0 1 4 1 2
Calculate the mean and median for each of the following data sets.(a) 3 7 4 11 5(b) 3 1 7 3 1
The following table lists values of the Consumer Price Index for 24 selected areas both for 2007 and 2001. Construct a five-stem display for the consumer price index in 2007.2007 2001 Anchorage 181 155 Atlanta 198 176 Boston 227 191 Chicago 198 178 Cincinnati 188 168 Cleveland 186 173 Dallas 195
If the double-stem display still has too few stems, we may wish to construct a stem-andleaf display with a separate stem to hold leaves 0 and 1, 2 and 3, 4 and 5, 6 and 7, and a stem to hold 8 and 9. The resulting stem-and-leaf display is called a five-stem display. The following is a five-digit
If there are too many leaves on some stems in a stem-and-leaf display, we might double the number of stems. The leaves 0–4 could hang on one stem and 5–9 on the repeated stem. For the observations 193 198 200 202 203 203 205 205 206 207 207 208 212 213 214 217 219 220 222 226 237 we would get
The following is a stem-and-leaf display with two-digit leaves. (The leading leaf digit 10.0.)1 2 46 68 93 3 19 44 71 82 97 4 05 26 43 90 5 04 68 6 13 List the corresponding measurements.
A federal government study of the oil reserves in Elk Hills, CA, included a stu Amount of Iron (percent ash)20 18 25 26 17 14 20 14 18 15 22 15 17 25 22 12 52 27 24 41 34 20 17 20 19 20 16 20 15 34 22 29 29 34 27 13 6 24 47 32 12 17 36 35 41 36 32 46 30 51 Make a stem-and-leaf display.
The following data represent the scores of 40 students on a college qualification test (courtesy of R.W. Johnson).162 171 138 145 144 126 145 162 174 178 167 98 161 152 182 136 165 137 133 143 184 166 115 115 95 190 119 144 176 135 194 147 160 158 178 162 131 106 157 154 Make a stem-and-leaf
The United States Geological Survey maintains data on large earthquakes including those of magnitude greater than 6.0 in California.Through 2008, the ordered magnitudes of the 55 quakes are 6.1 6.1 6.1 6.1 6.1 6.2 6.2 6.2 6.2 6.3 6.3 6.3 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.5 6.5 6.5 6.5 6.5 6.6 6.6 6.6
The weights (oz) of nineteen babies born in Madison, Wisconsin, are summarized in the computer output Descriptive Statistics: Weight Variable N Mean Median StDev Weight 19 118.05 117.00 15.47 Locate two measures of center tendency, or location, and interpret the values.
On a day, the noon temperature measurements(in °F) reported by five weather stations in a state were 74 80 76 76 73(a) Find the mean and median temperature in °F.(b) The Celsius (°C) scale is related to the Farenheit (°F) scale by C What are the mean and median temperatures in °C? (Answer
Some properties of the mean and median.1. If a fixed number c is added to all measurements in a data set, then the mean of the new measurements is c (the original mean).2. If all measurements in a data set are multiplied by a fixed numberd, then the mean of the new measurements is d (the
The speedy lizard data, from Exercise 2.19, are 1.28 1.36 1.24 2.47 1.94 2.52 2.67 1.29 1.56 2.66 2.17 1.57 2.10 2.54 1.63 2.11 2.57 1.72 0.76 1.02 1.78 0.50 1.49 1.57 1.04 1.92 1.55 1.78 1.70 1.20(a) Find the sample median, first quartile, and third quartile.(b) Find the sample 90th percentile.
With reference to Exercise 2.48, calculate the quartiles.
A large mail-order firm employs numerous persons to take phone orders. Computers on which orders are entered also automatically collect data on phone activity. One variable useful for planning staffing levels is the number of calls per shift handled by each employee.From the data collected on 25
Refer to the data of college qualification test scores given in Exercise 2.22.(a) Find the median.(b) Find and .
With reference to Exercise 2.3, calculate the quartiles.
The following measurements of the diameters(in feet) of Indian mounds in southern Wisconsin were gathered by examining reports in the Wisconsin Archeologist (courtesy of J.Williams).22 24 24 30 22 20 28 30 24 34 36 15 37(a) Create a dot diagram.(b) Calculate the mean and median and then mark these
Physical education researchers interested in the development of the overarm throw measured the horizontal velocity of a thrown ball at the time of release. The results for first-grade children (in feet/second) (courtesy of L.Halverson and M. Roberton) are Males 54.2 39.6 52.3 48.4 35.9 30.4 25.2
Loss of calcium is a serious problem for older women. To investigate the amount of loss, a researcher measured the initial amount of bone mineral content in the radius bone of the dominant hand of elderly women and then the amount remaining after one year. The differences, representing the loss of
Old Faithful, the most famous geyser in Yellowstone Park, had the following durations (measured in seconds) in six consecutive eruptions:240 248 113 268 117 253(a) Find the sample median.(b) Find the sample mean.
With reference to the number of returns in Example 3, obtain the sample (a) mean and(b) median.
Refer to the alligator data in Table D.11 of the Data Bank. Using the data on testosterone for male alligators:(a) Make separate dot plots for the Lake Apopka and Lake Woodruff alligators.(b) Calculate the sample means for each group.(c) Do the concentrations of testosterone appear to differ
A zoologist collected wild lizards in the Southwestern United States. Thirty lizards from the genus Phrynosoma were placed on a treadmill and their speed measured. The recorded speed (meters/second) is the fastest time to run a half meter. (Courtesy of K. Bonine.)1.28 1.36 1.24 2.47 1.94 2.52 2.67
The United States Environmental Protection Agency6 reports that in 2006, each American generated 4.6 pounds of solid waste a day.(a) Does this mean every single American produces the same amount of garbage? What do you think this statement means?(b) Was the number 4.6 obtained from a
Refer to the cause-and-effect diagram on page 17. The workers have now noticed that a delay could occur:(i) On the fourth floor at the pharmacy(ii) On the third floor at the practitioners’ station Redraw the diagram and include this added information.
According to the cause-and-effect diagram on page 17, where are the possible delays on the first floor?
Each year a local weekly newspaper gives out“Best of the City” awards in categories such as restaurant, deli, pastry shop, and so on. Readers are asked to fill in their favorites on a form enclosed in this free weekly paper and then send it to the publisher. The establishment receiving the most
It is often easy to put off doing an unpleasant task.At a Web site,5 persons can take a test and receive a score that determines if they have a serious problem with procrastination. Should the scores from people who take this test on-line be considered a random sample? Explain your reasoning.
Consider the population of persons living in Chicago. You want to learn about the proportion which are illegal aliens.(a) Specify the population unit.(b) Specify the variable of interest.(c) Specify the statistical population.
Cities must find better ways to dispose of solid waste. According to the Environmental Protection Agency, the composition of the 254 million tons of solid municipal waste created in 2007 was(a) Determine the percentage of other materials in the solid waste. This category includes glass, wood,
Tornadoes kill many people every year in the United States. The yearly number of lives lost during the 59 years 1950 through 2008 are summarized in the following table.Number of Deaths Frequency 24 or less 2 25–49 20 50–74 18 75–99 7 100–149 6 150–199 2 200–249 1 250 or more 3 Total
The city of Madison regularly checks the water quality at swimming beaches located on area lakes. The concentration of fecal coliforms, in number of colony forming units (CFU) per 100 ml of water, was measured on fifteen days during the summer at one beach.180 1600 90 140 50 260 400 90 380 110 10
Before microwave ovens are sold, the manufacturer must check to ensure that the radiation coming through the door is below a specified safe limit. The amounts of radiation leakage (mW/cm2) with the door closed from 25 ovens are as follows (courtesy of John Cryer):15 9 18 10 5 12 8 5 8 10 7 2 1 5 3
A person with asthma took measurements by blowing into a peak-flow meter on seven consecutive days.429 425 471 422 432 444 454 Display the data in a dot diagram.
A sample of 50 departing airline passengers at the main check-in counter produced the following number of bags checked through to final destinations.0 1 2 2 1 2 1 2 3 0 1 0 1 1 0 1 3 0 1 2 1 1 1 2 1 2 2 1 2 0 0 2 2 1 1 1 1 1 1 1 2 0 1 3 0 1 2 1 1 3(a) Make a relative frequency line diagram.(b)
A major West Coast power company surveyed 50 customers who were asked to respond to the statement, “People should rely mainly on themselves to solve problems caused by power outages” with one of the following responses.1. Definitely agree.2. Somewhat agree.3. Somewhat disagree.4. Definitely
Data from one campus dorm, on the number of complaints about the dorm food are collected each week of the semester. These weekly counts are to be grouped into the classes 0–1, 2–3, 4–5, 7 or more. Both endpoints are included.Explain where a difficulty might arise.
Data from one campus dorm on the number of burglaries are collected each week of the semester.These data are to be grouped into the classes 0–1, 2–3, 3–5, 6 or more. Both endpoints included. Explain where a difficulty might arise.
The number of automobile accidents reported per month helps to identify intersections that require improvement. Beginning January 2004 and ending November 2008, the number of crashes per month reported at an intersection near a university campus in Madison,Wisconsin, are 1 3 3 3 2 2 3 1 2 4 1 4 1 3
A student at the University of Wisconsin surveyed 40 students in her dorm concerning their participation in extracurricular activities during the past week. The data on number of activities are 1 5 0 1 4 3 0 2 1 6 1 1 0 0 2 0 0 3 1 2 1 2 2 2 2 2 1 0 2 2 3 4 2 7 2 2 3 3 1 1 Present these data in a
Recorded here are the blood types of 40 persons who have volunteered to donate blood at a plasma center. Summarize the data in a frequency table. Include calculations of the relative frequencies.O O A B A O A A A O B O B O O A O O A A A A AB A B A A O O A O O A A A O A O O AB
The following table shows the age at inauguration of each U.S. president.(a) Make a stem-and-leaf display with a double stem.(b) Find the median, Q1 and Q3.Age at Name Inauguration 1. Washington 57 2. J. Adams 61 3. Jefferson 57 4. Madison 57 5. Monroe 58 6. J. Q. Adams 57 7. Jackson 61 8. Van
The following are the numbers of passengers on the minibus tour of Hollywood.9 12 10 11 11 7 12 6 11 4 10 10 11 9 10 7 10 8 8 9 8 9 11 9 8 6 10 6 8 11(a) Find the sample median.(b) Find the sample mean.(c) Find the sample variance.
The stem-and-leaf display given here shows the final examination scores of students in a sociology course. (Leaf unit 1.0)Stem-and-Leaf Display of Scores 2 57 3 244 4 1179 5 03368 6 012447 7 223556899 8 00457 9 0036(a) Find the median score.(b) Find the quartiles and .(c) What proportion of the
The weights of twenty adult grizzly bears captured and released are summarized in the computer output Descriptive Statistics: bearwt Variable N Mean Median StDev Bearwt 20 227.4 232.5 82.7(a) Locate two measures of center tendency, or location, and interpret the values.(b) Locate the standard
Mung bean sprouts are more widely used in Asian cooking than the beans themselves. To study their growth, an experimenter presoaked some beans until they sprouted about 1 millimeter.Five were randomly selected and placed in individual petri dishes. After 96 hours, their lengths (mm)143 131 101 143
Table 13 gives data collected from the students attending an elementary statistics course at the University of Wisconsin. These data include sex, height, number of years in college, and the general area of intended major [Humanities(H); Social Science (S); Biological Science (B);Physical Science
Recorded here are the numbers of civilians employed in the United States by major occupationgroups for the years 2000 and 2007. (Source:Statistical Abstract of the United States, 2009.)(a) For each year, calculate the relative frequencies of the occupation groups.(b) Comment on changes in the
Make a control chart for the extraordinary event overtime data in Example 18 after removing the outlier identified in that example. You need to recalculate the mean and standard deviation.
Make a control chart of the data in Exercise 2.96 and comment.
The exchange rate between the United States and Canada can be stated as the number of Canadian dollars that can be purchased with$1. The official values for the year are 1998 1999 2000 2001 2002 2003 1.48 1.49 1.48 1.55 1.57 1.40 2004 2005 2006 2007 2008 1.30 1.21 1.13 1.07 1.07 Year 1992 1993 1994
Make a control chart for the data in Exercise 2.93 and comment.
Make a control chart for the data referred to in Exercise 2.92 and comment.
A city department has introduced a quality improvement program and has allowed employees to get credit for overtime hours when attending meetings of their quality groups.The total number of overtime meeting hours for each of the 26 pay periods in one year by row were 30 215 162 97 194 163 60 41 100
Refer to the class data in Exercise 2.100. Calculate the following.(a) and s for the heights of males.(b) and s for the heights of females.(c) Median and the quartiles for the heights of males.(d) Median and the quartiles for the heights of females.
The SAS computer software package produced the output on page 79. Compare the mean and standard deviation with that of the MINITAB output in Exercise 2.124. Which output gives more digits?
Find and s for the final times to run 1.5 miles in Table D.5 in the Data Bank.
Find and s for the data set in Table 4.
Lumber intended for building houses and other structures must be monitored for strength. The measurement of strength (pounds per square inch) for 61 specimens of Southern Pine (Source:U.S. Forest Products Laboratory) yielded 4001 3927 3048 4298 4000 3445 4949 3530 3075 4012 3797 3550 4027 3571 3738
With reference to the lightning data in Exercise 2.121,(a) Make a time plot of the data.(b) Comment on the appropriateness of presenting the mean and standard deviation as summaries.Calculations of the descriptive statistics such as and s are increasingly tedious with larger data sets. Current
Lightning causes many deaths each year in the United States. The yearly number of deaths for 50 years, 1959 through 2008 are, by rows, 183 129 149 153 165 129 149 110 88 129 131 122 122 94 124 102 91 74 98 88 63 74 66 77 77 67 74 68 88 68 67 74 73 41 43 69 85 53 42 44 46 51 44 51 43 32 38 47 45 27
The mode of a collection of observations is defined as the observed value with largest relative frequency. The mode is sometimes used as a center value. There can be more than one mode in a data set. Find the mode for the data given in Exercise 2.13.
The winning times of the men’s 400-meter freestyle swimming in the Olympics (1964 to 2008) appear in the following table.Winning Times in Minutes and Seconds Year Time 1964 4:12.2 1968 4:09.0 1972 4:00.27 1976 3:51.93 1980 3:51.31 1984 3:51.23 1988 3:46.95 1992 3:45.00 1996 3:47.97 2000 3:40.59
The following summary statistics were obtained from a data set.Approximately what proportion of the observations are:(a) Below 96.0?(b) Above 84.0?(c) In the interval 59.5 to 101.5?(d) In the interval 75.5 to 96.0?(e) In the interval 49.0 to 112.0?State which of your answers are based on the
To study how first-grade students utilize their time when assigned to a math task, a researcher observes 24 students and records their times off-task out of 20 minutes. The dotplot appears on page 3. (courtesy of T. Romberg).Times Off-Task (minutes)4 0 2 2 4 1 4 6 9 7 2 7 5 4 13 7 7 10 10 0 5 3 9 8
The data below were obtained from a detailed record of purchases of toothpaste over several years (courtesy of A. Banerjee). The usage times (in weeks) per ounce of toothpaste for a household taken from a consumer panel were.74 .45 .80 .95 .84 .82 .78 .82 .89 .75 .76 .81.85 .75 .89 .76 .89 .99 .71
In a genetic study, a regular food was placed in each of 20 vials and the number of flies of a particular genotype feeding on each vial recorded. The counts of flies were also recorded for another set of 20 vials that contained grape juice. The following data sets were obtained(courtesy of C.
Make a time plot of the phone call data in Exercise 2.48 and comment on the statistical control.
With reference to Exercise 2.90:(a) Calculate the median number of lost House seats.(b) Find the maximum and minimum losses and identify these with a President.(c) Determine the range for the number of House seats lost.
The weights (oz) of nineteen babies born in Madison, Wisconsin, are summarized in the computer output.Descriptive Statistics: Weight Variable N Mean Median StDev Weight 19 118.05 117.00 15.47 Variable Minimum Maximum Q1 Q3 Weight 89.00 144.00 106.00 131.00(a) Locate a measure of variation and also
Recent crime reports on the number of aggravated assaults at each of the 27 largest universities reporting for the year are summarized in the computer output.Descriptive Statistics: AggAslt Variable N Mean Median StDev AggAslt 27 10.30 10.00 7.61 Variable Minimum Maximum Q1 Q3 AggAslt 0.00 29.00
A sample of seven compact discs at the music store stated the performance times as lasting the following numbers of minutes for Beethoven’s Ninth Symphony.66.9 66.2 71.0 68.6 65.4 68.4 71.9(a) Find the sample median.(b) Find the sample mean.(c) Find the sample standard deviation.
With reference to the data on the length of 10 major league baseball games in Exercise 2.43:(a) Find the sample mean.(b) Find the sample variance.(c) Find the sample standard deviation.2.70 With reference to checked bags in Exercise 2.13,(a) Find the sample mean.(b) Find the sample standard
The city of Madison regularly checks the quality of water at swimming beaches located on area lakes. Fifteen times the concentration of fecal coliforms, in number of colony forming units (CFU) per 100 ml of water, was measured during the summer at one beach.180 1600 90 140 50 260 400 90 380 110 10
A campus area merchant recorded the number of bad checks received per month, for five months 4 5 4 7 6 Calculate:(a) The sample variance.(b) The sample standard deviation.
Find the standard deviation of the measurements of diameters given in Exercise 2.45.
The monthly rents for 7 one-bedroom apartments located in one area of the city, are 625 740 805 670 705 740 870(a) Give two possible factors that may contribute to variation in the monthly rents.Calculate(b) The sample variance.(c) The sample standard deviation.
For each data set, calculate .(a) 1 4 3 2 2(b) 2 1 1 3 0 2(c) 9 8 8 9 8 8 9
For the data of Exercise 2.59, calculate by using the alternative formula.
For the data of Exercise 2.57, calculate by using the alternative formula.
Repeat (a) and (b) of Exercise 2.59 for the data set 2.5 1.7 2.1 1.5 1.7
Repeat (a) and (b) of Exercise 2.57 for the data set 4 9 2

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