A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
13th Edition
ISBN: 9780135183885
Author: Rick Billstein, Shlomo Libeskind, Johnny Lott, Barbara Boschmans
Publisher: PEARSON
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Chapter 5.2A, Problem 29A
To determine
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The temperature drop in 8 hours using integers.
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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…
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…
Chapter 5 Solutions
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Ch. 5.1 - Prob. 1MCCh. 5.1 - Prob. 2MCCh. 5.1 - Prob. 3MCCh. 5.1 - Prob. 4MCCh. 5.1 - Prob. 5MCCh. 5.1 - Prob. 6MCCh. 5.1 - Describe a realistic word problem that models...Ch. 5.1 - Prob. 8MCCh. 5.1 - a. I chose an integer. I then subtract 10 from the...Ch. 5.1 - Investigate how tides are measured and design an...
Ch. 5.1 - Prob. 11MCCh. 5.1 - Prob. 12MCCh. 5.1 - A fourth-grade student devised the following...Ch. 5.1 - Prob. 14MCCh. 5.1 - MATHEMATICAL CONNECTIONS A student had the...Ch. 5.1 - Prob. 16MCCh. 5.1 - Prob. 17MCCh. 5.1 - Prob. 18MCCh. 5.1 - On the School Book Page on p. 244, complete the...Ch. 5.1 - Prob. 1NAEPCh. 5.1 - Prob. 2NAEPCh. 5.1A - Find the additive inverse of each of the following...Ch. 5.1A - Simplify each of the following expressions. a. (2)...Ch. 5.1A - Evaluate each of the following expressions. a. |5|...Ch. 5.1A - Use the absolute value definition of addition to...Ch. 5.1A - Demonstrate each of the following additions using...Ch. 5.1A - Demonstrate each of the in exercise 5 following...Ch. 5.1A - Use a No. Line Model to compute the following...Ch. 5.1A - Use chip Model to compute the following...Ch. 5.1A - Prob. 9ACh. 5.1A - Prob. 10ACh. 5.1A - In each of following problems, write an addition...Ch. 5.1A - The Cowboys football team lost 6 yards on their...Ch. 5.1A - In golf, par is a score of zero. If you go over...Ch. 5.1A - Compute each of following expression. a. 2+(310)...Ch. 5.1A - In each of following problems, write both a...Ch. 5.1A - Simplify each of the following expressions as much...Ch. 5.1A - For which integers a, b and c does ab+c=a(bc)?...Ch. 5.1A - Place the integers 4,3,2,0,1,2,3,4 in the grid to...Ch. 5.1A - Let y=x1. Find the value of y in parts a-d when x...Ch. 5.1A - Determine the number of terms in the arithmetic...Ch. 5.1A - How could you explain the time change from the...Ch. 5.1A - Find all integer x, if there are any, such that...Ch. 5.1A - In each of the following equations, find all...Ch. 5.1A - An arithmetic sequence may have a positive or...Ch. 5.1A - Classify each of the following as true or false...Ch. 5.1A - Solve the following equations. a. x+7=3 b. 10+x=7...Ch. 5.1B - ASSESSMENT Find the additive inverse of each of...Ch. 5.1B - ASSESSMENT Simplify each of the following...Ch. 5.1B - ASSESSMENT Evaluate each of the following...Ch. 5.1B - Prob. 4ACh. 5.1B - Prob. 9ACh. 5.1B - ASSESSMENT In each of the following problems,...Ch. 5.1B - ASSESSMENT In each of the following problems,...Ch. 5.1B - Prob. 12ACh. 5.1B - Prob. 13ACh. 5.1B - ASSESSMENT Compute each of the following. a....Ch. 5.1B - Prob. 15ACh. 5.1B - ASSESSMENT Simplify each of the following...Ch. 5.1B - Prob. 17ACh. 5.1B - Prob. 18ACh. 5.1B - ASSESSMENT Let y=3x2. Find the value of y in parts...Ch. 5.1B - ASSESSMENT Determine the number of terms in the...Ch. 5.1B - Prob. 21ACh. 5.1B - ASSESSMENT Find all integers x, if there are any,...Ch. 5.1B - ASSESSMENT Let y=|x5|. Find the value of y in...Ch. 5.1B - ASSESSMENT An arithmetic sequence may have a...Ch. 5.1B - ASSESSMENT Classify each of the following as true...Ch. 5.1B - Prob. 26ACh. 5.2 - Explain whether (xy)(x+y) can be multiplied by...Ch. 5.2 - We use the equation (a+b)2=a2+2ab+b2 to find a...Ch. 5.2 - Consider the argument to show that (a)(b)=(ab) for...Ch. 5.2 - Prob. 4MCCh. 5.2 - Explain how to find the number of integers between...Ch. 5.2 - Prob. 6MCCh. 5.2 - The Swiss mathematician Leonhard Euler 1707-1783...Ch. 5.2 - Prob. 8MCCh. 5.2 - Prob. 10MCCh. 5.2 - Prob. 11MCCh. 5.2 - If n is an odd integer, is n2 even or odd? Justify...Ch. 5.2 - A seventh-grade student does not believe 52.The...Ch. 5.2 - A student computes 82(3) by writing 10(3)=30. How...Ch. 5.2 - Prob. 15MCCh. 5.2 - Mariyana felt that using absolute values with...Ch. 5.2 - In solving the problems 325, Annie changes it to...Ch. 5.2 - Prob. 18MCCh. 5.2 - Think about the Convince Me on page 261 and if it...Ch. 5.2 - Prob. 20MCCh. 5.2 - Prob. 21MCCh. 5.2 - Prob. 22MCCh. 5.2 - Prob. 23MCCh. 5.2 - Prob. 1NAEPCh. 5.2 - Prob. 2NAEPCh. 5.2 - Prob. 3NAEPCh. 5.2 - Prob. 4NAEPCh. 5.2A - Use patterns to show that (1)(1)=1Ch. 5.2A - Use the chip model to show the following. a)...Ch. 5.2A - Use the number line model to show that 2(4)=8Ch. 5.2A - In each of the following chip models, the...Ch. 5.2A - The number of students eating in the school...Ch. 5.2A - Use the definition of division to find each...Ch. 5.2A - Evaluate each of the following expressions, if...Ch. 5.2A - Evaluate each of the following products and then,...Ch. 5.2A - In each of the following, x and y are integers;y0....Ch. 5.2A - In a lab, the temperature of various chemical...Ch. 5.2A - The farmland acreage lost to family dwellings over...Ch. 5.2A - Illustrate the distributive property of...Ch. 5.2A - Compute each of the following. a. (2)3 b. (2)4 c....Ch. 5.2A - If x is an integer and x0, which of the following...Ch. 5.2A - Find all integer values of x for which the...Ch. 5.2A - If 48x is an integer and x is an integer what are...Ch. 5.2A - Identify the property of integers being...Ch. 5.2A - Prob. 18ACh. 5.2A - Multiply each of the following and combine terms...Ch. 5.2A - Find all integers x if any each of the following....Ch. 5.2A - Use the difference-of-squares formula to simplify...Ch. 5.2A - Factor each of the following expressions...Ch. 5.2A - Prob. 23ACh. 5.2A - In each of the following, find the next two terms....Ch. 5.2A - Find the missing terms in the following arithmetic...Ch. 5.2A - A hot air balloon descends at the rate of...Ch. 5.2A - A paper cup is 7in. tall with 1in. of that height...Ch. 5.2A - A scuba diver descended 450feet in 15 minutes at a...Ch. 5.2A - Prob. 29ACh. 5.2A - Your Sirius radio bill is 40 each month. You have...Ch. 5.2A - Prob. 31ACh. 5.2A - Prob. 32ACh. 5.2A - Uncle Bob has a debt of 2000. His five siblings...Ch. 5.2B - Use patterns to show that (2)(2)=4.Ch. 5.2B - Use the chip model to show the following. a....Ch. 5.2B - Prob. 3ACh. 5.2B - Prob. 4ACh. 5.2B - Prob. 5ACh. 5.2B - Prob. 6ACh. 5.2B - Prob. 7ACh. 5.2B - Prob. 8ACh. 5.2B - Prob. 9ACh. 5.2B - Prob. 10ACh. 5.2B - Prob. 11ACh. 5.2B - Prob. 12ACh. 5.2B - Compute each of the following. a. 10312 b. 10(312)...Ch. 5.2B - Prob. 14ACh. 5.2B - Prob. 15ACh. 5.2B - If 54x is an integer and x is an integer, what are...Ch. 5.2B - Identify the property of integers being...Ch. 5.2B - The quotient of two integers is 4. List four...Ch. 5.2B - Multiply each of the following and combine terms...Ch. 5.2B - Find all integers x if any that make the...Ch. 5.2B - Use the difference of squares formula to simplify...Ch. 5.2B - Factor each of the following expressions...Ch. 5.2B - Prob. 23ACh. 5.2B - In each of the following, find the next two terms....Ch. 5.2B - Prob. 25ACh. 5.2B - Prob. 26ACh. 5.2B - Prob. 27ACh. 5.2B - Prob. 28ACh. 5.2B - Prob. 29ACh. 5.2B - Jose has 250 in his bank account. His cell phone...Ch. 5.2B - Lake Mead is at an all-time low water level. The...Ch. 5.2B - Prob. 32ACh. 5.2B - Prob. 33ACh. 5.CR - Find the additive inverse of each of the...Ch. 5.CR - Prob. 2CRCh. 5.CR - For each of the following, find all possible...Ch. 5.CR - Prob. 4CRCh. 5.CR - Prob. 5CRCh. 5.CR - Prob. 6CRCh. 5.CR - Prob. 7CRCh. 5.CR - Prob. 8CRCh. 5.CR - Prob. 9CRCh. 5.CR - Prob. 10CRCh. 5.CR - The average high temperature in July in Barrow,...Ch. 5.CR - Prob. 12CRCh. 5.CR - Les has hiking Death Valley and began her hike at...Ch. 5.CR - Brian plays on his college golf team. Last spring...Ch. 5.CR - Two golfers completed one round of golf. The first...Ch. 5.CR - Roman civilization began in 509BCE and ended in...Ch. 5.CR - Pythagoras was born about 570BCE. Isaac Newton was...Ch. 5.CR - Prob. 18CRCh. 5.CR - Simplify each of the following expressions. a. 1x...Ch. 5.CR - Prob. 20CRCh. 5.CR - Prob. 21CRCh. 5.CR - Prob. 22CRCh. 5.CR - Prob. 23CRCh. 5.CR - Prob. 24CRCh. 5.CR - Prob. 25CRCh. 5.CR - Prob. 26CRCh. 5.CR - Prob. 27CRCh. 5.CR - Prob. 28CRCh. 5.CR - Prob. 29CRCh. 5.CR - Prob. 30CRCh. 5.CR - Prob. 31CRCh. 5.CR - Prob. 32CRCh. 5.CR - Prob. 33CRCh. 5.CR - The drawing below depicts an elevator. Explain...Ch. 5.CR - Prob. 35CRCh. 5.CR - Prob. 36CRCh. 5.CR - Prob. 37CRCh. 5.CR - Prob. 38CRCh. 5.CR - Prob. 39CRCh. 5.CR - Prob. 40CRCh. 5.CR - Prob. 41CRCh. 5.CR - Prob. 42CRCh. 5.CR - Prob. 43CRCh. 5.CR - Prob. 44CRCh. 5.CR - Prob. 45CRCh. 5.CR - Prob. 46CRCh. 5.CR - Prob. 47CRCh. 5 - Now Try this 1 Explain whether the sum of two...Ch. 5 - Now Try this 2 Model the subtraction 43 on a...Ch. 5 - Prob. 3NT
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- rounded to two decimal places at each calculationarrow_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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