MATLAB: An Introduction with Applications
5th Edition
ISBN: 9781118629864
Author: Amos Gilat
Publisher: WILEY
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Chapter 1, Problem 13P
Two
For each part, verify that the identity is correct by calculating the values of the left and right sides of the equation, substituting x = 24°.
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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
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1
1029
2
1686
3
2269
4
2675
5
3487
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4652
7
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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 1 Solutions
MATLAB: An Introduction with Applications
Ch. 1 - Prob. 1PCh. 1 - Calculate: 4125.22e5100.53 1323+ln5008Ch. 1 - Calculate: (a) 14.836.3213+52 (b)...Ch. 1 - Calculate: 24.5+64/3.52+8.312.5376.428/15...Ch. 1 - Calculate: a. cos7x9+tan715sin15 b....Ch. 1 - Define the variable xas x = 6.7, then evaluate: a....Ch. 1 - Define the variable tas t = 3.2, then evaluate:...Ch. 1 - Define the variables x and y as x = 5.1 and y =...Ch. 1 - Define the variables a, b, c, and d as:...Ch. 1 - Prob. 10P
Ch. 1 - Prob. 11PCh. 1 - Two trigonometric identities are given by:...Ch. 1 - Two trigonometric identities are given by:...Ch. 1 - Define two variables: alpha=/6 , and beta=3/8 ....Ch. 1 - Given: xsinaxdx=sinaxa2xcosaxa . Use MATLAB to...Ch. 1 - In the triangle shown a=5.3in.,=42,andb=6 in....Ch. 1 - In the triangle shown a = 5 in., b = 7 in., and =...Ch. 1 - In the ice cream cone shown, L = 4 in. and =35 ....Ch. 1 - Prob. 19PCh. 1 - The parametric equations of a line in space are:...Ch. 1 - The circumference of an ellipse can be...Ch. 1 - 315 people have to be transported using buses that...Ch. 1 - 739 apples are to be packed and shipped such that...Ch. 1 - Assign the number 316,501.673 to a variable, and...Ch. 1 - Prob. 25PCh. 1 - Prob. 26PCh. 1 - Prob. 27PCh. 1 - Prob. 28PCh. 1 - Prob. 29PCh. 1 - Prob. 30PCh. 1 - Radioactive decay of carbon-14 is used for...Ch. 1 - The greatest common divisor is the largest...Ch. 1 - The Moment Magnitude Scale (MMS), denoted Mw,...Ch. 1 - Prob. 34PCh. 1 - Prob. 35PCh. 1 - Newton’s law of cooling gives the temperature T(t)...Ch. 1 - The stress intensity factor K predicts the stress...Ch. 1 - Prob. 38PCh. 1 - Use the Help Window to find a display format that...Ch. 1 - Prob. 40P
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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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