Essentials of Statistics Plus MyLab Statistics with Pearson eText - Access Card Package (5th Edition)
5th Edition
ISBN: 9780133864960
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 4.2, Problem 1BSC
Florida Lottery Let A denote the
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For unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months (Bureau of Labor Statistics, January 2010). Suppose the following data are for a particular region in upstate New York. The values in the first column show the number of
months unemployed and the values in the second column show the corresponding number of unemployed persons.
Months
Unemployed
Number
Unemployed
1
1029
2
1686
3
2269
4
2675
5
3487
6
4652
7
4145
8
3587
9
2325
10
1120
Let x be a random variable indicating the number of months a person is unemployed.
a. Use the data to develop an empirical discrete probability distribution for x (to 4 decimals).
(x)
f(x)
1
2
3
4
5
6
7
8
9
10
b. Show that your probability distribution satisfies the conditions for a valid discrete probability distribution.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
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c. What is the probability that a…
West Virginia has one of the highest divorce rates in the nation, with an annual rate of approximately 5 divorces per 1000 people (Centers for Disease Control and Prevention website, January 12, 2012). The Marital Counseling Center, Inc. (MCC) thinks that the high divorce rate in the state may require them to hire additional staff.
Working with a consultant, the management of MCC has developed the following probability distribution for x = the number of new clients for marriage counseling for the next year.
Excel File: data05-19.xls
x
10
f(x)
.05
20
30
.10
.10
40
.20
50
60
.35
.20
a. Is this probability distribution valid?
- Select your answer-
Explain.
f(x)
Σf(x)
Select your answer
Select your answer
b. What is the probability MCC will obtain more than 30 new clients (to 2 decimals)?
c. What is the probability MCC will obtain fewer than 20 new clients (to 2 decimals)?
d. Compute the expected value and variance of x.
Expected value
Variance
clients per year
squared clients per year
For unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months (Bureau of Labor Statistics, January 2010). Suppose the following data are for a particular region in upstate New York. The values in the first column show the number of
months unemployed and the values in the second column show the corresponding number of unemployed persons.
Months
Unemployed
Number
Unemployed
1
1029
2
1686
3
2269
4
2675
5
3487
6
4652
7
4145
8
3587
9
2325
10
1120
Let x be a random variable indicating the number of months a person is unemployed.
a. Use the data to develop an empirical discrete probability distribution for x (to 4 decimals).
(x)
f(x)
1
2
3
4
5
6
7
8
9
10
b. Show that your probability distribution satisfies the conditions for a valid discrete probability distribution.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
c. What is the probability that a person…
Chapter 4 Solutions
Essentials of Statistics Plus MyLab Statistics with Pearson eText - Access Card Package (5th Edition)
Ch. 4.2 - Florida Lottery Let A denote the event of placing...Ch. 4.2 - Probability Given that the following statement is...Ch. 4.2 - Interpreting Weather While this exercise was being...Ch. 4.2 - Subjective Probability Estimate the probability...Ch. 4.2 - Prob. 5BSCCh. 4.2 - Prob. 6BSCCh. 4.2 - Prob. 7BSCCh. 4.2 - Prob. 8BSCCh. 4.2 - In Exercises 912, assume that 400 births are...Ch. 4.2 - In Exercises 912, assume that 400 births are...
Ch. 4.2 - In Exercises 912, assume that 400 births are...Ch. 4.2 - In Exercises 912, assume that 400 births are...Ch. 4.2 - Traffic Light When arriving at the traffic light...Ch. 4.2 - Weather While this exercise was being created,...Ch. 4.2 - In Exercises 1320, express the indicated degree of...Ch. 4.2 - Pierced Ears Based on a Harris poll, there is a...Ch. 4.2 - SAT Test When making a random guess for an answer...Ch. 4.2 - Dice When rolling a pair of dice at the Bellagio...Ch. 4.2 - Statistics Test It is impossible to pass a...Ch. 4.2 - In Exercises 1320, express the indicated degree of...Ch. 4.2 - Pre-Employment Drug Screening Find the probability...Ch. 4.2 - Pre-Employment Drug Screening Hind the probability...Ch. 4.2 - Table 4-1 Pre-Employment Drug Screening Results...Ch. 4.2 - Table 4-1 Pre-Employment Drug Screening Results...Ch. 4.2 - In Exercises 2532, find the probability and answer...Ch. 4.2 - In Exercises 2532, find the probability and answer...Ch. 4.2 - Struck by Lightning In a recent year, 304 of the...Ch. 4.2 - In Exercises 2532, find the probability and answer...Ch. 4.2 - In Exercises 2532, find the probability and answer...Ch. 4.2 - Using Probability to Identify Unlikely Events. In...Ch. 4.2 - Using Probability to Identify Unlikely Events. In...Ch. 4.2 - Using Probability to Identify Unlikely Events. In...Ch. 4.2 - Using Probability to Identify Unlikely Events. In...Ch. 4.2 - Using Probability to Identify Unlikely Events. In...Ch. 4.2 - Using Probability to Identify Unlikely Events. In...Ch. 4.2 - Using Probability to Identify Unlikely Events. In...Ch. 4.2 - Probability from a Sample Space. In Exercises...Ch. 4.2 - Probability from a Sample Space. In Exercises...Ch. 4.2 - Two Children Exercise 37 lists the sample spice...Ch. 4.2 - Probability from a Sample Space. In Exercises...Ch. 4.2 - In Exercises 2532, find the probability and answer...Ch. 4.2 - In Exercises 2532, find the probability and answer...Ch. 4.2 - Prob. 43BBCh. 4.2 - Finding Odds in Roulette A roulette wheel has 38...Ch. 4.2 - Prob. 45BBCh. 4.2 - Prob. 46BBCh. 4.2 - Relative Risk and Odds Ratio In a clinical trial...Ch. 4.3 - Complements What is wrong with the expression?...Ch. 4.3 - Casino Craps A gambler plans to play the casino...Ch. 4.3 - Disjoint Events For a Gallup poll, M is the event...Ch. 4.3 - Rule of Complements One form of the rule of...Ch. 4.3 - Determining Whether Events Are Disjoint. For...Ch. 4.3 - Determining Whether Events Are Disjoint. For...Ch. 4.3 - Determining Whether Events Are Disjoint. For...Ch. 4.3 - Determining Whether Events Are Disjoint. For...Ch. 4.3 - Determining Whether Events Are Disjoint. For...Ch. 4.3 - Determining Whether Events Are Disjoint. For...Ch. 4.3 - Determining Whether Events Are Disjoint. For...Ch. 4.3 - Determining Whether Events Are Disjoint. For...Ch. 4.3 - Whatever A Marist poll survey showed that 47% of...Ch. 4.3 - Online Courses According to the National...Ch. 4.3 - Flirting Survey In a Microsoft Instant Messaging...Ch. 4.3 - Finding Complements. In Exercises 58, find the...Ch. 4.3 - Drug Screening If one of the test subjects is...Ch. 4.3 - Drug Screening If one of the test subjects is...Ch. 4.3 - Drug Screening If one of the subjects it randomly...Ch. 4.3 - Drug Screening If one of the subjects is randomly...Ch. 4.3 - Dosage Calculations. In Exercises 2126, use the...Ch. 4.3 - Dosage Calculations. In Exercises 2126, use the...Ch. 4.3 - Dosage Calculations. In Exercises 2126, use the...Ch. 4.3 - Dosage Calculations. In Exercises 2126, use the...Ch. 4.3 - Dosage Calculations. In Exercises 2126, use the...Ch. 4.3 - Dosage Calculations. In Exercises 2126, use the...Ch. 4.3 - Survey Refusals. In Exercises 2732, refer to the...Ch. 4.3 - Survey Refusals. In Exercises 2732, refer to the...Ch. 4.3 - Survey Refusals. In Exercises 2732, refer to the...Ch. 4.3 - Survey Refusals. In Exercises 2732, refer to the...Ch. 4.3 - Prob. 31BSCCh. 4.3 - Survey Refusals. In Exercises 2732, refer to the...Ch. 4.3 - In Exercises 3338, use these results from the...Ch. 4.3 - In Exercises 3338, use these results from the...Ch. 4.3 - In Exercises 3338, use these results from the...Ch. 4.3 - In Exercises 3338, use these results from the...Ch. 4.3 - In Exercises 3338, use these results from the...Ch. 4.3 - In Exercises 3338, use these results from the...Ch. 4.3 - Gender Selection When analyzing results from a...Ch. 4.3 - Disjoint Events If events A and B are disjoint and...Ch. 4.3 - Exclusive Or The formal addition rule expressed...Ch. 4.3 - Extending the Addition Rule Extend the formal...Ch. 4.3 - Complements and the Addition Rule a. Develop a...Ch. 4.4 - Notation Let R be the event of randomly selecting...Ch. 4.4 - Independent and Dependent Events Are events R and...Ch. 4.4 - Independent and Dependent Events True or false:...Ch. 4.4 - Sample for a Poll There are currently 28,741,346...Ch. 4.4 - Independent and Dependent Events. In Exercises...Ch. 4.4 - Independent and Dependent Events. In Exercises...Ch. 4.4 - Independent and Dependent Events. In Exercises...Ch. 4.4 - Independent and Dependent Events. In Exercises...Ch. 4.4 - Independent and Dependent Events. In Exercises...Ch. 4.4 - Independent and Dependent Events. In Exercises...Ch. 4.4 - Independent and Dependent Events. In Exercises...Ch. 4.4 - Independent and Dependent Events. In Exercises...Ch. 4.4 - Pro-Employment Drug Screening. In Exercises 1316,...Ch. 4.4 - Pre-Employment Drug Screening. In Exercises 1316,...Ch. 4.4 - Pre-Employment Drug Screening. In Exercises 1316,...Ch. 4.4 - Pre-Employment Drug Screening. In Exercises 1316,...Ch. 4.4 - Acceptance Sampling With one method of a procedure...Ch. 4.4 - Acceptance Sampling With one method of a procedure...Ch. 4.4 - Redundancy In Computer Hard Drives It is generally...Ch. 4.4 - Redundancy In Aircraft Radios The FAA requires...Ch. 4.4 - Born on the 4th of July For the following, ignore...Ch. 4.4 - Hiring Employees Assume that Google, Inc. hires...Ch. 4.4 - In Exercises 2326, use these results from the...Ch. 4.4 - In Exercises 2326, use these results from the...Ch. 4.4 - In Exercises 2326, use these results from the...Ch. 4.4 - Prob. 26BSCCh. 4.4 - In Exercises 2730, find the probabilities and...Ch. 4.4 - In Exercises 2730, find the probabilities and...Ch. 4.4 - Prob. 29BSCCh. 4.4 - In Exercises 2730, find the probabilities and...Ch. 4.4 - System Reliability Refer to the figure at the top...Ch. 4.4 - Prob. 32BBCh. 4.5 - Prob. 1BSCCh. 4.5 - Prob. 2BSCCh. 4.5 - Prob. 3BSCCh. 4.5 - Confusion of the Inverse Using the same events A...Ch. 4.5 - Describing Complements. In Exercises 58, provide a...Ch. 4.5 - Describing Complements. In Exercises 58, provide a...Ch. 4.5 - Describing Complements. In Exercises 58, provide a...Ch. 4.5 - Describing Complements. In Exercises 58, provide a...Ch. 4.5 - At Least One Correct Answer If you make random...Ch. 4.5 - At Least One Working Calculator A statistics...Ch. 4.5 - Probability of a Girl Assuming that boys and girls...Ch. 4.5 - At Least One Correct Answer If you make random...Ch. 4.5 - Births in the United States hi the United States,...Ch. 4.5 - Births in China In China, the probability of a...Ch. 4.5 - Car Crashes The probability of a randomly selected...Ch. 4.5 - Cleared Burglaries According 10 FBI data, 12.4% of...Ch. 4.5 - At Least One. In Exercises 5-12, find the...Ch. 4.5 - Compliments at Work Based on a poll conducted...Ch. 4.5 - In Exercises 19-24, refer to Table 4-1, included...Ch. 4.5 - In Exercises 19-24, refer to Table 4-1, included...Ch. 4.5 - In Exercises 19-24, refer to Table 4-1, included...Ch. 4.5 - In Exercises 19-24, refer to Table 4-1, included...Ch. 4.5 - In Exercises 19-24, refer to Table 4-1, included...Ch. 4.5 - In Exercises 19-24, refer to Table 4-1, included...Ch. 4.5 - Identical and Fraternal Twins. In Exercises 25-28,...Ch. 4.5 - Identical and Fraternal Twins. In Exercises 25-28,...Ch. 4.5 - Prob. 27BSCCh. 4.5 - Prob. 28BSCCh. 4.5 - Redundancy in Computer Hard Drives Assume that...Ch. 4.5 - Prob. 30BSCCh. 4.5 - Composite Drug Screening Based on the data in...Ch. 4.5 - Composite Water Samples The Fairfield County...Ch. 4.5 - Prob. 33BBCh. 4.5 - Prob. 34BBCh. 4.6 - Prob. 1BSCCh. 4.6 - Prob. 2BSCCh. 4.6 - California Daily 4 The winning numbers for the...Ch. 4.6 - Selections with Replacement When randomly...Ch. 4.6 - In Exercises 5-36, express all probabilities as...Ch. 4.6 - In Exercises 5-36, express all probabilities as...Ch. 4.6 - In Exercises 5-36, express all probabilities as...Ch. 4.6 - In Exercises 5-36, express all probabilities as...Ch. 4.6 - Prob. 9BSCCh. 4.6 - Prob. 10BSCCh. 4.6 - Prob. 11BSCCh. 4.6 - Prob. 12BSCCh. 4.6 - Prob. 13BSCCh. 4.6 - Prob. 14BSCCh. 4.6 - Prob. 15BSCCh. 4.6 - Florida Lottery Winning the jackpot in the Florida...Ch. 4.6 - Prob. 17BSCCh. 4.6 - Prob. 18BSCCh. 4.6 - Prob. 19BSCCh. 4.6 - Prob. 20BSCCh. 4.6 - Prob. 21BSCCh. 4.6 - Prob. 22BSCCh. 4.6 - In Exercises 5-36, express all probabilities as...Ch. 4.6 - Prob. 24BSCCh. 4.6 - Jumble Puzzle Many newspapers carry Jumble, a...Ch. 4.6 - Jumble Puzzle Many newspapers carry Jumble, a...Ch. 4.6 - Prob. 27BSCCh. 4.6 - Prob. 28BSCCh. 4.6 - Electricity When testing for current in a cable...Ch. 4.6 - Prob. 30BSCCh. 4.6 - Prob. 31BSCCh. 4.6 - In Exercises 5-36, express all probabilities as...Ch. 4.6 - Prob. 33BSCCh. 4.6 - Prob. 34BSCCh. 4.6 - Prob. 35BSCCh. 4.6 - Prob. 36BSCCh. 4.6 - Prob. 37BBCh. 4.6 - Prob. 38BBCh. 4.6 - Prob. 39BBCh. 4.6 - Prob. 40BBCh. 4 - A multiple-choice question on a statistics quiz...Ch. 4 - As the author is creating this exercise, a weather...Ch. 4 - Prob. 3CQQCh. 4 - Prob. 4CQQCh. 4 - Estimate the probability that a randomly selected...Ch. 4 - Prob. 6CQQCh. 4 - In Exercises 6-10, use site following results from...Ch. 4 - Prob. 8CQQCh. 4 - In Exercises 6-10, use site following results from...Ch. 4 - Prob. 10CQQCh. 4 - Prison and Plea. In Exercises 1-10, use the data...Ch. 4 - Prison and Plea. In Exercises 1-10, use the data...Ch. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prison and Plea. In Exercises 1-10, use the data...Ch. 4 - Prison and Plea. In Exercises 1-10, use the data...Ch. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Trifecta In horse racing, a trifecta is a bet that...Ch. 4 - Prob. 1CRECh. 4 - Unusual/Unlikely Events a. The mean pulse rate for...Ch. 4 - Prob. 3CRECh. 4 - Prob. 4CRECh. 4 - Sampling Eye Color Based on a study by Dr. P....Ch. 4 - Prob. 6CRECh. 4 - Prob. 7CRECh. 4 - Prob. 1FDDCh. 4 - Prob. 2FDDCh. 4 - Prob. 3FDDCh. 4 - Prob. 4FDDCh. 4 - Prob. 5FDDCh. 4 - Prob. 6FDDCh. 4 - Prob. 7FDDCh. 4 - Critical Thinking: Interpreting medical test...Ch. 4 - Prob. 9FDD
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- In Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1014 adults aged 18 and over. One of the questions was "How many cups of coffee, if any, do you drink on an average day?" The following table shows the results obtained (Gallup website, August 6, 2012). Excel File: data05-23.xls Number of Cups per Day Number of Responses 0 365 264 193 3 4 or more 91 101 Define a random variable x = number of cups of coffee consumed on an average day. Let x = 4 represent four or more cups. Round your answers to four decimal places. a. Develop a probability distribution for x. x 0 1 2 3 4 f(x) b. Compute the expected value of x. cups of coffee c. Compute the variance of x. cups of coffee squared d. Suppose we are only interested in adults that drink at least one cup of coffee on an average day. For this group, let y = the number of cups of coffee consumed on an average day. Compute the expected value of y. Compare it to the expected value of x. The…arrow_forwardIn Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1014 adults aged 18 and over. One of the questions was "How many cups of coffee, if any, do you drink on an average day?" The following table shows the results obtained (Gallup website, August 6, 2012). Excel File: data05-23.xls Number of Cups per Day Number of Responses 0 365 264 193 2 3 4 or more 91 101 Define a random variable x = number of cups of coffee consumed on an average day. Let x = 4 represent four or more cups. Round your answers to four decimal places. a. Develop a probability distribution for x. x 0 1 2 3 f(x) b. Compute the expected value of x. cups of coffee c. Compute the variance of x. cups of coffee squared d. Suppose we are only interested in adults that drink at least one cup of coffee on an average day. For this group, let y = the number of cups of coffee consumed on an average day. Compute the expected value of y. Compare it to the expected value of x. The…arrow_forwardA technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types of malfunctions occur at about the same frequency. Develop a probability distribution for the duration of a service call. Duration of Call x f(x) 1 2 3 4 Which of the following probability distribution graphs accurately represents the data set? Consider the required conditions for a discrete probability function, shown below.Does this probability distribution satisfy equation (5.1)?Does this probability distribution satisfy equation (5.2)? What is the probability a service call will take three hours? A service call has just come in, but the type of malfunction is unknown. It is 3:00 P.M. and service technicians usually get off at 5:00 P.M. What is the probability the service technician will have to work overtime to fix the machine today?arrow_forward
- A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let x be a random variable indicating the number of sessions required to gain the patient's trust. The following probability function has been proposed. x f(x) for x = 1, 2, or 3 a. Consider the required conditions for a discrete probability function, shown below. f(x) ≥0 Σf(x) = 1 (5.1) (5.2) Does this probability distribution satisfy equation (5.1)? Select Does this probability distribution satisfy equation (5.2)? Select b. What is the probability that it takes exactly 2 sessions to gain the patient's trust (to 3 decimals)? c. What is the probability that it takes at least 2 sessions to gain the patient's trust (to 3 decimals)?arrow_forwardA technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types of malfunctions occur at about the same frequency. Develop a probability distribution for the duration of a service call. Which of the following probability distribution graphs accurately represents the data set? Consider the required conditions for a discrete probability function, shown below.Does this probability distribution satisfy equation (5.1)?Does this probability distribution satisfy equation (5.2)? What is the probability a service call will take three hours? A service call has just come in, but the type of malfunction is unknown. It is 3:00 P.M. and service technicians usually get off at 5:00 P.M. What is the probability the service technician will have to work overtime to fix the machine today?arrow_forwardWest Virginia has one of the highest divorce rates in the nation, with an annual rate of approximately 5 divorces per 1000 people (Centers for Disease Control and Prevention website, January 12, 2012). The Marital Counseling Center, Inc. (MCC) thinks that the high divorce rate in the state may require them to hire additional staff. Working with a consultant, the management of MCC has developed the following probability distribution for x = the number of new clients for marriage counseling for the next year. Excel File: data05-19.xls 10 20 f(x) .05 .10 11 30 40 50 60 .10 .20 .35 .20 a. Is this probability distribution valid? Yes Explain. greater than or equal to 0 f(x) Σf(x) equal to 1 b. What is the probability MCC will obtain more than 30 new clients (to 2 decimals)? c. What is the probability MCC will obtain fewer than 20 new clients (to 2 decimals)? d. Compute the expected value and variance of x. Expected value Variance clients per year squared clients per yeararrow_forward
- Reconsider the patient satisfaction data in Table 1. Fit a multiple regression model using both patient age and severity as the regressors. (a) Test for significance of regression. (b) Test for the individual contribution of the two regressors. Are both regressor variables needed in the model? (c) Has adding severity to the model improved the quality of the model fit? Explain your answer.arrow_forwardThe output voltage of a power supply is assumed to be normally distributed. Sixteen observations taken at random on voltage are as follows: 10.35, 9.30, 10.00, 9.96, 11.65, 12.00, 11.25, 9.58, 11.54, 9.95, 10.28, 8.37, 10.44, 9.25, 9.38, and 10.85. (a) Test the hypothesis that the mean voltage equals 12 V against a two-sided alternative using a = 0.05. (b) Construct a 95% two-sided confidence interval on μ. (c) Test the hypothesis that σ² = 11 using α = 0.05. (d) Construct a 95% two-sided confidence interval on σ. (e) Construct a 95% upper confidence interval on σ. (f) Does the assumption of normality seem reasonable for the output voltage?arrow_forwardAnalyze the residuals from the regression model on the patient satisfaction data from Exercise 3. Comment on the adequacy of the regression model.arrow_forward
- Consider the hypotheses: Hop=po H₁ppo where 2 is known. Derive a general expression for determining the sample size for detecting a true mean of 1μo with probability 1-ẞ if the type I error is a.arrow_forwardSuppose we wish to test the hypotheses: Họ : | = 15 H₁: 15 where we know that o² = 9.0. If the true mean is really 20, what sample size must be used to ensure that the probability of type II error is no greater than 0.10? Assume that a = 0.05.arrow_forwardTable 1 contains the data from a patient satisfaction survey for a group of 25 randomly selected patients at a hospital. In addition to satisfaction, data were collected on patient age and an index that measured the severity of illness. (a) Fit a linear regression model relating satisfaction to patient age. (b) Test for significance of regression. (c) What portion of the total variability is accounted for by the regressor variable age? Table 1: Patient Satisfaction Data Severity Observation Age (21) (x2) Satisfaction (y) 1 55 50 2 46 24 3 30 46 4 35 48 5 59 58 6 61 60 7 74 65 8 38 42 9 27 42 10 51 50 11 53 38 12 41 30 13 37 31 88 14 24 34 15 42 30 16 50 48 17 58 61 18 60 71 19 62 62 20 68 38 21 70 41 22 79 66 23 63 31 24 39 42 25 49 40 BE225222222222222222 68 77 96 80 43 44 26 88 75 57 56 88 102 88 70 43 46 56 59 26 83 75arrow_forward
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