ALEKS 360 ELEM STATISTICS
10th Edition
ISBN: 9781264241385
Author: Bluman
Publisher: MCG
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Chapter 5.2, Problem 9E
Automobiles A survey shows 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.
blank
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 5 Solutions
ALEKS 360 ELEM STATISTICS
Ch. 5.1 - Dropping College Courses Use the following table...Ch. 5.1 - Define and give three examples of a random...Ch. 5.1 - Explain the difference between a discrete and a...Ch. 5.1 - Give three examples of a discrete random variable.Ch. 5.1 - Give three examples of a continuous random...Ch. 5.1 - List three continuous random variables and three...Ch. 5.1 - What is a probability distribution? Give an...Ch. 5.1 - For Exercises 7 through 12, determine whether the...Ch. 5.1 - For Exercises 7 through 12, determine whether the...Ch. 5.1 - For Exercises 7 through 12, determine whether the...
Ch. 5.1 - For Exercises 7 through 12, determine whether the...Ch. 5.1 - For Exercises 7 through 12, determine whether the...Ch. 5.1 - For Exercises 7 through 12, determine whether the...Ch. 5.1 - For Exercises 13 through 18, state whether the...Ch. 5.1 - For Exercises 13 through 18, state whether the...Ch. 5.1 - For Exercises 13 through 18, state whether the...Ch. 5.1 - For Exercises 13 through 18, state whether the...Ch. 5.1 - For Exercises 13 through 18, state whether the...Ch. 5.1 - For Exercises 13 through 18, state whether the...Ch. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - Triangular Numbers The first six triangular...Ch. 5.1 - Child Play in Day Care In a popular day care...Ch. 5.1 - Goals in Hockey The probability that a hockey team...Ch. 5.1 - Mathematics Tutoring Center At a drop-in...Ch. 5.1 - For Exercises 31 through 36, write the...Ch. 5.1 - For Exercises 31 through 36, write the...Ch. 5.1 - For Exercises 31 through 36, write the...Ch. 5.1 - For Exercises 31 through 36, write the...Ch. 5.1 - For Exercises 31 through 36, write the...Ch. 5.1 - For Exercises 31 through 36, write the...Ch. 5.1 - Computer Games The probability that a child plays...Ch. 5.2 - Radiation Exposure On March 28, 1979, the nuclear...Ch. 5.2 - Coffee with Meals A researcher wishes to determine...Ch. 5.2 - Suit Sales The number of suits sold per day at a...Ch. 5.2 - Daily Newspapers A survey was taken of the number...Ch. 5.2 - Trivia Quiz The probabilities that a player will...Ch. 5.2 - New Homes A contractor has four new home plans....Ch. 5.2 - Traffic Accidents The county highway department...Ch. 5.2 - Fitness Machine A fitness center bought a new...Ch. 5.2 - Benfords Law The leading digits in actual data,...Ch. 5.2 - Automobiles A survey shows the probability of the...Ch. 5.2 - Pizza Deliveries A pizza shop owner determines the...Ch. 5.2 - Grab Bags A convenience store has made up 20 grab...Ch. 5.2 - Job Bids A landscape contractor bids on jobs where...Ch. 5.2 - Rolling Dice If a person rolls doubles when she...Ch. 5.2 - Dice Game A person pays 2 to play a certain game...Ch. 5.2 - Lottery Prizes A lottery offers one 1000 prize,...Ch. 5.2 - Winning the Lottery For a daily lottery, a person...Ch. 5.2 - Life Insurance A 35-year-old woman purchases a...Ch. 5.2 - Roulette A roulette wheel has 38 numbers, 1...Ch. 5.2 - Rolling Dice Construct a probability distribution...Ch. 5.2 - Rolling a Die When one die is rolled, the expected...Ch. 5.2 - The formula for finding the variance for a...Ch. 5.2 - Complete the following probability distribution if...Ch. 5.2 - Probability Distribution A bag contains five balls...Ch. 5.3 - Unsanitary Restaurants Health officials routinely...Ch. 5.3 - Which of the following are binomial experiments or...Ch. 5.3 - Which of the following are binomial experiments or...Ch. 5.3 - Compute the probability of X successes, using...Ch. 5.3 - Compute the probability of X successes, using...Ch. 5.3 - Compute the probability of X successes, using the...Ch. 5.3 - Compute the probability of X successes, using the...Ch. 5.3 - Belief in UFOs A survey found that 10% of...Ch. 5.3 - Multiple-Choice Exam A student takes a...Ch. 5.3 - High Blood Pressure Twenty percent of Americans...Ch. 5.3 - High School Dropouts Approximately 10.3% of...Ch. 5.3 - Advertising Three out of four people think most...Ch. 5.3 - Language Spoken at Home by the U.S. Population In...Ch. 5.3 - Prison Inmates Forty percent of prison inmates...Ch. 5.3 - Destination Weddings Twenty-six percent of couples...Ch. 5.3 - People Who Have Some College Education Fifty-three...Ch. 5.3 - Guidance Missile System A missile guidance system...Ch. 5.3 - Find the mean, variance, and standard deviation...Ch. 5.3 - Find the mean, variance, and standard deviation...Ch. 5.3 - Airline Accidents Twenty-five percent of...Ch. 5.3 - Tossing Coins Find the mean, variance, and...Ch. 5.3 - American and Foreign-Born Citizens In 2014 the...Ch. 5.3 - Federal Government Employee E-mail Use It has been...Ch. 5.3 - Watching Fireworks A survey found that 21% of...Ch. 5.3 - Alternate Sources of Fuel Eighty-five percent of...Ch. 5.3 - Survey on Bathing Pets A survey found that 25% of...Ch. 5.3 - Survey on Answering Machine Ownership In a survey,...Ch. 5.3 - Poverty and the Federal Government One out of...Ch. 5.3 - Internet Purchases Thirty-two percent of adult...Ch. 5.3 - Prob. 29ECh. 5.3 - Job Elimination In a recent year, 13% of...Ch. 5.3 - Survey of High School Seniors Of graduating high...Ch. 5.3 - Is this a binomial distribution? Explain.Ch. 5.3 - Children in a Family The graph shown here...Ch. 5.3 - Construct a binomial distribution graph for the...Ch. 5.3 - Show that the mean for a binomial random variable...Ch. 5.4 - Rockets and Targets During the latter days of...Ch. 5.4 - Use the multinomial formula and find the...Ch. 5.4 - Use the multinomial formula and find the...Ch. 5.4 - MMs Color Distribution According to the...Ch. 5.4 - Truck Inspection Violations The probabilities are...Ch. 5.4 - Prob. 5ECh. 5.4 - Mendels Theory According to Mendels theory, if...Ch. 5.4 - Find each probability P(X; ), using Table C in...Ch. 5.4 - Find each probability P(X; ) using Table C in...Ch. 5.4 - Study of Robberies A recent study of robberies for...Ch. 5.4 - Misprints on Manuscript Pages In a 400-page...Ch. 5.4 - Colors of Flowers A nursery provides red impatiens...Ch. 5.4 - Mail Ordering A mail-order company receives an...Ch. 5.4 - Company Mailing Of a companys mailings 1.5% are...Ch. 5.4 - Emission Inspection Failures If 3% of all cars...Ch. 5.4 - Phone Inquiries The average number of phone...Ch. 5.4 - Defective Calculators In a batch of 2000...Ch. 5.4 - School Newspaper Staff A school newspaper staff is...Ch. 5.4 - Job Applicants Twelve people apply for a teaching...Ch. 5.4 - Prob. 19ECh. 5.4 - Defective Computer Keyboards A shipment of 24...Ch. 5.4 - Defective Electronics A shipment of 24 smartphones...Ch. 5.4 - Job Applications Ten people apply for a job at...Ch. 5.4 - Auto Repair Insurance A person calls people to ask...Ch. 5.4 - Prob. 24ECh. 5.4 - Shooting an Arrow Mark shoots arrows at a target...Ch. 5.4 - Amusement Park Game At an amusement park...Ch. 5.4 - Prob. 27ECCh. 5.4 - Prob. 28ECCh. 5.4 - Drawing Cards Cards are drawn at random from a...Ch. 5.4 - Prob. 30ECCh. 5.4 - Prob. 31ECCh. 5.4 - Lessons Outside of School About 2 out of every 3...Ch. 5.4 - Prob. 33ECCh. 5.4 - Work versus Conscience One worker in four in...Ch. 5 - For Exercises 1 through 3, determine whether the...Ch. 5 - For Exercises 1 through 3, determine whether the...Ch. 5 - Prob. 5.1.3RECh. 5 - Prob. 5.1.4RECh. 5 - Credit Cards A large retail company encourages its...Ch. 5 - Prob. 5.1.6RECh. 5 - Shoe Purchases At Shoe World, the manager finds...Ch. 5 - Prob. 5.2.8RECh. 5 - Arrivals at an Airport At a small rural airport,...Ch. 5 - Cans of Paint Purchased During a recent paint sale...Ch. 5 - Phone Customers A phone service center keeps track...Ch. 5 - Outdoor Regatta A producer plans an outdoor...Ch. 5 - Card Game A game is set up as follows: All the...Ch. 5 - Card Game Using Exercise 13, how much should be...Ch. 5 - Let x be a binomial random variable with n = 12...Ch. 5 - Internet Access via Cell Phone In a retirement...Ch. 5 - Self-Driving Automobile Fifty-eight percent of...Ch. 5 - Prob. 5.3.18RECh. 5 - U.S. Police Chiefs and the Death Penalty The...Ch. 5 - Prob. 5.3.20RECh. 5 - Pizza for Breakfast Three out of four American...Ch. 5 - Prob. 5.3.22RECh. 5 - Prob. 5.4.23RECh. 5 - Prob. 5.4.24RECh. 5 - Accounting Errors The probability that an...Ch. 5 - Prob. 5.4.26RECh. 5 - Prob. 5.4.27RECh. 5 - Boating Accidents The number of boating accidents...Ch. 5 - Prob. 5.4.29RECh. 5 - Prob. 5.4.30RECh. 5 - Items Donated to a Food Bank At a food bank a case...Ch. 5 - Prob. 5.4.32RECh. 5 - Prob. 5.4.33RECh. 5 - Determine whether each statement is true or false....Ch. 5 - Determine whether each statement is true or false....Ch. 5 - Determine whether each statement is true or false....Ch. 5 - Determine whether each statement is true or false....Ch. 5 - Complete these statements with the best answer. 5....Ch. 5 - Complete these statements with the best answer. 6....Ch. 5 - Complete these statements with the best answer. 7....Ch. 5 - Select the best answer. 8. What is the sum of the...Ch. 5 - Select the best answer. 9. How many outcomes are...Ch. 5 - Select the best answer. 10. The number of trials...Ch. 5 - Prob. 11CQCh. 5 - Prob. 12CQCh. 5 - For exercises 11 through 14, determine if the...Ch. 5 - For exercises 11 through 14, determine if the...Ch. 5 - Prob. 15CQCh. 5 - Prob. 16CQCh. 5 - Prob. 17CQCh. 5 - Calls for a Crisis Hot Line The number of calls...Ch. 5 - Selecting a Card There are 6 playing cards placed...Ch. 5 - Prob. 20CQCh. 5 - Carpooling If 40% of all commuters ride to work in...Ch. 5 - Employed Women If 60% of all women are employed...Ch. 5 - Prob. 23CQCh. 5 - Meeting Attendance A history class has 75 members....Ch. 5 - Prob. 25CQCh. 5 - Quality Control Check Before a television set...Ch. 5 - Bowling Team Uniforms Among the teams in a bowling...Ch. 5 - Elm Trees If 8% of the population of trees are elm...Ch. 5 - Sports Score Hot Line Calls Sports Scores Hot Line...Ch. 5 - Color of Raincoats There are 48 raincoats for sale...Ch. 5 - Youth Group Officers A youth group has 8 boys and...Ch. 5 - Blood Types About 4% of the citizens of the United...Ch. 5 - Alcohol Abstainers About 35% of Americans abstain...Ch. 5 - Prob. 1CTCCh. 5 - Prob. 2CTCCh. 5 - Prob. 3CTCCh. 5 - Prob. 4CTCCh. 5 - Prob. 5CTC
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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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