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introduction to probability statistics
Questions and Answers of
Introduction To Probability Statistics
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
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,
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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)
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
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
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
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
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
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)
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
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,
A campus area merchant recorded the number of bad checks received per month, for five months 4 5 4 7 6 Display the data in a dot diagram.
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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.
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
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
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.
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
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
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
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
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
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
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
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
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
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
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