ALEKS 360 ELEM STATISTICS
10th Edition
ISBN: 9781264241385
Author: Bluman
Publisher: MCG
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Textbook Question
Chapter 3.2, Problem 27E
Missing Work The average number of days that construction workers miss per year is 11. The standard deviation is 2.3. The average number of days that factory workers miss per year is 8 with a standard deviation of 1.8. Which class is more variable in terms of days missed?
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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
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…
A 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?
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)?
Chapter 3 Solutions
ALEKS 360 ELEM STATISTICS
Ch. 3.1 - Teacher Salaries The following data from several...Ch. 3.1 - Roller Coaster Speeds The data show the heights in...Ch. 3.1 - Airport Parking The number of short-term parking...Ch. 3.1 - Length of School Years The lengths of school years...Ch. 3.1 - Observers in the Frogwatch Program The number of...Ch. 3.1 - Top Video Games The following represent XBOX One...Ch. 3.1 - Earnings of Nonliving Celebrities Forbes magazine...Ch. 3.1 - Paid Days Off The data show the number of paid...Ch. 3.1 - Top-Paid CEOs The data shown are the total...Ch. 3.1 - Airline Passengers The data show a sample of the...
Ch. 3.1 - Foreign Workers The number of foreign workers...Ch. 3.1 - Distances of Stars Of the 25 brightest stars, the...Ch. 3.1 - Contest Spelling Words The last words given and...Ch. 3.1 - Wind Speeds The data show the maximum wind speeds...Ch. 3.1 - Hourly Compensation for Production Workers The...Ch. 3.1 - Points in Rose Bowl Games The data show the number...Ch. 3.1 - Percentage of Foreign-Born People The percentage...Ch. 3.1 - Percentage of College-Educated Population over 25...Ch. 3.1 - Net Worth of Corporations These data represent the...Ch. 3.1 - Specialty Coffee Shops A random sample of 30...Ch. 3.1 - Commissions Earned This frequency distribution...Ch. 3.1 - Children of U.S. Presidents The data show the...Ch. 3.1 - Enrollments for Selected Independent Religiously...Ch. 3.1 - Automobile Selling Prices Find the weighted mean...Ch. 3.1 - Fat Grams Using the weighted mean, find the...Ch. 3.1 - Diet Cola Preference A recent survey of a new diet...Ch. 3.1 - Costs of Helicopters The costs of three models of...Ch. 3.1 - Final Grade An instructor grades exams, 20%; term...Ch. 3.1 - Final Grade Another instructor gives four 1-hour...Ch. 3.1 - For these situations, state which measure of...Ch. 3.1 - Describe which measure of central tendencymean,...Ch. 3.1 - What types of symbols are used to represent sample...Ch. 3.1 - A local fast-food company claims that the average...Ch. 3.1 - If the mean of five values is 64, find the sum of...Ch. 3.1 - If the mean of five values is 8.2 and four of the...Ch. 3.1 - Find the mean of 10, 20, 30, 40, and 50. a. 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- A 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_forwardReconsider 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_forward
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