Introductory Statistics
1st Edition
ISBN: 9781938168208
Author: Barbara Illowsky, Susan Dean
Publisher: OpenStax College
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Chapter 2, Problem 34P
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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 2 Solutions
Introductory Statistics
Ch. 2 - For the Park City basketball team, scores for the...Ch. 2 - The following data show the distances (in miles)...Ch. 2 - The table shows the number of sins and losses the...Ch. 2 - In a survey, 40 people were asked how many times...Ch. 2 - The population in Park City is made up of...Ch. 2 - Park city is broken down into six voting...Ch. 2 - The following data are the shoe sizes of 50 male...Ch. 2 - The following data are the number of sports played...Ch. 2 - The following data represent the number of...Ch. 2 - Construct a frequency polygon of U.S. Presidents’...
Ch. 2 - The following table is a portion of a data set...Ch. 2 - For the following 11 salaries, calculate the IQR...Ch. 2 - Find the interquartile range for the following two...Ch. 2 - Forty bus drivers were asked how many hours they...Ch. 2 - Refer to the Table 223. Find the third quartile....Ch. 2 - Listed are 29 ages for Academy Award sinning best...Ch. 2 - Listed are 30 ages for Academy Award winning best...Ch. 2 - For the 100-meter dash, the third quartile for...Ch. 2 - On a 60 point written assignment, the 80th...Ch. 2 - During a season, the 40th percentile for points...Ch. 2 - The following data are the number of pages In 40...Ch. 2 - The folloising data set show’s the heights in...Ch. 2 - Follow the steps you used to graph a...Ch. 2 - The following data show the number of months...Ch. 2 - In a sample of 60 households, one house is worth...Ch. 2 - The number of books checked out from the library...Ch. 2 - Five credit scores are 680, 680, 700, 720, 720....Ch. 2 - Mails conducted a study on the effect that playing...Ch. 2 - Discuss the mean, median, and mode for each of the...Ch. 2 - On a baseball team, the ages of each of the...Ch. 2 - The following data show the different types of pet...Ch. 2 - Find the standard deviation for the data from the...Ch. 2 - Two swimmers, Angie and Beth, from different...Ch. 2 - For each of the following data sets, create a stem...Ch. 2 - For each of the following data sets, create a stem...Ch. 2 - For each of the following data sets, create a stem...Ch. 2 - For each of the following data sets, create a stem...Ch. 2 - For each of the following data sets, create a stem...Ch. 2 - For each of the following data sets, create a stem...Ch. 2 - For each of the following data sets, create a stem...Ch. 2 - The students in Ms. Ramirez’s math class have...Ch. 2 - Using the data from Mrs. Ramirez’s math class...Ch. 2 - David County has six high schools. Each school...Ch. 2 - Use the data from the David County science...Ch. 2 - Sixty-five randomly selected car salespersons were...Ch. 2 - What does the frequency column in Table 2.42 sum...Ch. 2 - What does the relative frequency column in Table...Ch. 2 - What is the difference between relative frequency...Ch. 2 - What is the difference between cumulative relative...Ch. 2 - To construct the histogram for the data in Table...Ch. 2 -
Ch. 2 - Construct a frequency polygon from the frequency...Ch. 2 - Use the two frequency tables to compare the life...Ch. 2 - Construct a times series graph for (a) the number...Ch. 2 - The following data sets List full time police per...Ch. 2 - Listed are 29 ages for Academy Award winning best...Ch. 2 - Listed are 32 ages for Academy Award winning best...Ch. 2 - Jesse was ranked 37th in his graduating class of...Ch. 2 - a. For runners in a race, a low time means a...Ch. 2 - a. For runners in a race, a higher speed means a...Ch. 2 - On an exam, would it be more desirable to earn a...Ch. 2 - Mina is waiting in line at the Department of Motor...Ch. 2 - In a survey collecting data about the salaries...Ch. 2 - In a study collecting data about the repair costs...Ch. 2 - The University of California has two criteria used...Ch. 2 - Suppose that you are buying a house. You and your...Ch. 2 - First quartile = _______Ch. 2 - Second quartile = median = 50th percentile =Ch. 2 - Third quartile = _______Ch. 2 - Interquartile range (IQR) = _____ — _____Ch. 2 - Inteiquartile range (IQR = _____ — _____ = _____...Ch. 2 - percentile = _______Ch. 2 - Use the following information to answer the next...Ch. 2 - Use the following information to answer the next...Ch. 2 - Find the mean for the following frequency tables.Ch. 2 - Use the following information to answer the next...Ch. 2 - Use the following information to answer the next...Ch. 2 - Use the following information to answer the next...Ch. 2 - Use the following information to answer the next...Ch. 2 - Use the following information to answer the next...Ch. 2 - Use the following information to answer the next...Ch. 2 - Use the following information to answer the next...Ch. 2 - Use the following information to answer the next...Ch. 2 - Use the following information to answer the next...Ch. 2 - When the data are skewed left, what is the typical...Ch. 2 - When the data are symmetrical, what is the typical...Ch. 2 - What word describes a distribution that has two...Ch. 2 - Describe the shape of this distribution. Figure...Ch. 2 - Describe the relationship between the mode and the...Ch. 2 - Describe the relationship between the mean and the...Ch. 2 - Describe the shape of this distribution. Figure...Ch. 2 - Describe the relationship between the mode and the...Ch. 2 - Are the mean and the median the exact same in this...Ch. 2 - Describe the shape of this distribution. Figure...Ch. 2 - Describe the relationship between the mode and the...Ch. 2 - Describe the relationship between the mean and the...Ch. 2 - The mean and median for the data are the same. 3;...Ch. 2 - Which is the greatest, the mean, the mode, or the...Ch. 2 - Which is the least, the mean, the mode, and the...Ch. 2 - Of the three measures, which tends to reflect...Ch. 2 - In a perfectly symmetrical distribution, when...Ch. 2 - Use the following information to answer the next...Ch. 2 - Use the following information to answer the next...Ch. 2 - Two baseball players, Fredo and Karl, on different...Ch. 2 - Use Table 2.57 to find the value that is three...Ch. 2 - Find the standard deviation for the following...Ch. 2 - Student grades on a chemistry exam were: 77, 78,...Ch. 2 - Table 2.61 contains the 2010 obesity rates in U.S....Ch. 2 - Suppose that three book publishers were interested...Ch. 2 - Often, cruise ships conduct all on-board...Ch. 2 - Twenty-five randomly selected students were asked...Ch. 2 - The percentage of people who own at most three...Ch. 2 - If the data were collected by asking the first 111...Ch. 2 - Following are the 2010 obesity rates by U.S....Ch. 2 - The median age for U.S. blacks currently is 30.9...Ch. 2 - Six hundred adult Americans were asked by...Ch. 2 - Given the following box plot: Figure 2.41 a. which...Ch. 2 - The following box plot shows the U.S. population...Ch. 2 - In a survey of 2O-year-olds in China, Germany, and...Ch. 2 - Given the following box plot, answer the...Ch. 2 - Given the following box plots, answer t*...Ch. 2 - A survey was conducted of 130 purchases of new BMW...Ch. 2 - Twenty-five randomly selected students were asked...Ch. 2 - The most obese countries in the world have obesity...Ch. 2 - Table 2.72 gives the percent of children under...Ch. 2 - The median age of the U.S. population in 1980 was...Ch. 2 - Use the following information to answer the neat...Ch. 2 - Use the following information to answer the neat...Ch. 2 - Use the following information to answer the neat...Ch. 2 - Use the following information to answer the neat...Ch. 2 - Use the following information to answer the neat...Ch. 2 - Use the following information to answer the neat...Ch. 2 - Use the following information to answer the neat...Ch. 2 - Use the following information to answer the neat...Ch. 2 - Use the following information to answer the neat...Ch. 2 - Three students were applying to the same graduate...Ch. 2 - A music school has budgeted to purchase three...Ch. 2 - An elementary school class ran one mile with a...Ch. 2 - The most obese countries in the world have obesity...Ch. 2 - Table 2.76 gives the percent of children under...Ch. 2 - Santa, Clara Country, Ca, has approximately 27,873...Ch. 2 - Javier and Ercilia are supervisors at a shopping...Ch. 2 - What is the IQR? a. 8 b. 11 C. 15 d. 35Ch. 2 - What is the mode? a. 19 b. 19.5 c. 1and 20 d....Ch. 2 - Is this a sample or the entire population? a....Ch. 2 - Twenty-five randomly selected students were asked...Ch. 2 - Forty randomly selected students were asked the...Ch. 2 - Following are the published weights (in pounds) of...Ch. 2 - One hundred teachers attended a seminar on...Ch. 2 - Refer to Figure 2.50 determine which of the...Ch. 2 - In a recent issue of the IFFF Spectrum, 84...Ch. 2 - A survey of enrollment at 35 community colleges...Ch. 2 - Use the following information to answer the next...Ch. 2 - Use the following information to answer the not...Ch. 2 - Suppose that a publisher conducted a survey asking...
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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
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