Intro Stats, Books a la Carte Edition (5th Edition)
5th Edition
ISBN: 9780134210285
Author: Richard D. De Veaux, Paul Velleman, David E. Bock
Publisher: PEARSON
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Chapter 5, Problem 4E
Placement exams An incoming freshman took her college’s placement exams in French and mathematics. In French, she scored 82 and in math 86. The overall results on the French exam had a
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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
Intro Stats, Books a la Carte Edition (5th Edition)
Ch. 5.1 - Your statistics teacher has announced that the...Ch. 5.1 - A distribution of incomes shows a strongly right...Ch. 5.2 - Prob. 3JCCh. 5.2 - Prob. 4JCCh. 5.3 - As a group, the Dutch are among the tallest people...Ch. 5.3 - Prob. 6JCCh. 5.3 - The mean of our original sample of 100 commute...Ch. 5.3 - Prob. 8JCCh. 5 - Stats test The mean score on the Stats exam was 75...Ch. 5 - Mensa People with z-scores above 2.5 on an IQ test...
Ch. 5 - Temperatures A towns January high temperatures...Ch. 5 - Placement exams An incoming freshman took her...Ch. 5 - Shipments A company selling clothing on the...Ch. 5 - Hotline A companys customer service hotline...Ch. 5 - Prob. 7ECh. 5 - Prob. 8ECh. 5 - Guzzlers? Environmental Protection Agency (EPA)...Ch. 5 - IQ Some IQ tests are standardized to a Normal...Ch. 5 - Prob. 11ECh. 5 - Stats test Suppose your statistics professor...Ch. 5 - Normal cattle The Virginia Cooperative Extension...Ch. 5 - IQs revisited Based on the Normal model N(100, 15)...Ch. 5 - ACT scores The Mathematics section of the ACT test...Ch. 5 - Prob. 16ECh. 5 - Prob. 17ECh. 5 - Wisconsin ACT 2015 The histogram shows the...Ch. 5 - Payroll Here are the summary statistics for the...Ch. 5 - Hams A specialty foods company sells gourmet hams...Ch. 5 - Prob. 21ECh. 5 - Prob. 22ECh. 5 - Prob. 23ECh. 5 - Windy In the last chapter, we looked at three...Ch. 5 - Prob. 25ECh. 5 - Combining scores again The first Stat exam had a...Ch. 5 - Final exams Anna, a language major, took final...Ch. 5 - Prob. 28ECh. 5 - Prob. 29ECh. 5 - Car speeds 100 John Beale of Stanford, California,...Ch. 5 - Prob. 31ECh. 5 - Prob. 32ECh. 5 - Prob. 33ECh. 5 - Prob. 34ECh. 5 - Prob. 35ECh. 5 - Prob. 36ECh. 5 - Small steer In Exercise 29, we suggested the model...Ch. 5 - Prob. 38ECh. 5 - Trees A forester measured 27 of the trees in a...Ch. 5 - Rivets A company that manufactures rivets believes...Ch. 5 - Prob. 41ECh. 5 - Car speeds 100, the picture For the car speed data...Ch. 5 - Winter Olympics 2014 Thirty-four men completed the...Ch. 5 - Check the model The mean of the 100 car speeds in...Ch. 5 - Receivers 2015 NFL data from the 2015 football...Ch. 5 - Prob. 46ECh. 5 - Prob. 47ECh. 5 - Prob. 48ECh. 5 - More cattle Based on the model N(1152, 84)...Ch. 5 - More IQs In the Normal model N(100, 15) from...Ch. 5 - Prob. 51ECh. 5 - IQ, finis Consider the IQ model N(100, 15) one...Ch. 5 - Cholesterol Assume the cholesterol levels of adult...Ch. 5 - Tires A tire manufacturer believes that the...Ch. 5 - Kindergarten Companies that design furniture for...Ch. 5 - Prob. 56ECh. 5 - Eggs Hens usually begin laying eggs when they are...Ch. 5 - Tomatoes Agricultural scientists are working on...
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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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