Introduction to the Practice of Statistics
9th Edition
ISBN: 9781319013387
Author: David S. Moore, George P. McCabe, Bruce A. Craig
Publisher: W. H. Freeman
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Question
Chapter 4.3, Problem 60E
(a)
To determine
To test: Whether the area under the curve is 1 or not.
(a)
Expert Solution
Answer to Problem 60E
Solution: Yes, the area under the curve is 1.
Explanation of Solution
Calculation: The area of a triangle is,
The height is 1 and the base is equal to 2. Thus, the area can be calculated as:
Hence, the area is 1. The provided curve is shown below:
(b)
Section 1:
To determine
To find: The
(b)
Section 1:
Expert Solution
Answer to Problem 60E
Solution: The probability is 0.5.
Explanation of Solution
Calculation: First, obtain the area in the interval of
In the graph, the total area is 1 and the dotted area which is also called the density of the curve. Thus, the area of
Now, the probability of Y is less than 1 can be calculated as:
Hence, the probability is 0.5.
Section 2:
To determine
To graph: The density curve and shade the area which represents the probability.
Section 2:
Expert Solution
Explanation of Solution
Graph: In the provided triangle, draw a vertical line at 1. Construct a triangle on the left end of the triangle and shade the left area. Hence, the density curve is shown below:
Section 3:
To determine
To find: The area.
Section 3:
Expert Solution
Answer to Problem 60E
Solution: The area is 0.5.
Explanation of Solution
Calculation: From the provided triangle, base is equal to 1 and height is equal to 1. Thus, the area can be calculated as:
Hence, the area is 0.5.
(c)
Section 1:
To determine
To find: The probability
(c)
Section 1:
Expert Solution
Answer to Problem 60E
Solution: The probability is 0.875.
Explanation of Solution
First, obtain the area in the interval of
base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated by the formula:
The area of
Now, the probability of Y is greater than 1.5 can be calculated as:
Hence, the probability is 0.875.
Section 2:
To determine
To graph: The density curve and shade the area which represents the probability.
Section 2:
Expert Solution
Explanation of Solution
Graph: In the provided triangle, draw a vertical line at 1.5. Construct a triangle on the right end of the triangle and shade the left area. Hence, the density curve is shown below:
Section 3:
To determine
To find: The area.
Section 3:
Expert Solution
Answer to Problem 60E
Solution: The area is 0.125.
Explanation of Solution
Calculation: From the provided triangle, base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated as:
Hence, the area is 0.125.
(d)
To determine
To find: The probability
(d)
Expert Solution
Answer to Problem 60E
Solution: The probability is 0.875.
Explanation of Solution
Calculation: First, obtain the area in the interval of
The area of
Now, the probability of Y is greater than 0.5 can be calculated as:
Hence, the probability is 0.875.
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Chapter 4 Solutions
Introduction to the Practice of Statistics
Ch. 4.1 - Prob. 1UYKCh. 4.1 - Prob. 2ECh. 4.1 - Prob. 3ECh. 4.1 - Prob. 4ECh. 4.1 - Prob. 5ECh. 4.1 - Prob. 6ECh. 4.1 - Prob. 7ECh. 4.2 - Prob. 8UYKCh. 4.2 - Prob. 9UYKCh. 4.2 - Prob. 10UYK
Ch. 4.2 - Prob. 11UYKCh. 4.2 - Prob. 12UYKCh. 4.2 - Prob. 13UYKCh. 4.2 - Prob. 14UYKCh. 4.2 - Prob. 15UYKCh. 4.2 - Prob. 16UYKCh. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - Prob. 20ECh. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 - Prob. 24ECh. 4.2 - Prob. 25ECh. 4.2 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.2 - Prob. 40ECh. 4.2 - Prob. 41ECh. 4.3 - Prob. 42UYKCh. 4.3 - Prob. 43UYKCh. 4.3 - Prob. 44UYKCh. 4.3 - Prob. 45ECh. 4.3 - Prob. 46ECh. 4.3 - Prob. 47ECh. 4.3 - Prob. 48ECh. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - Prob. 52ECh. 4.3 - Prob. 53ECh. 4.3 - Prob. 54ECh. 4.3 - Prob. 55ECh. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - Prob. 59ECh. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.4 - Prob. 63UYKCh. 4.4 - Prob. 64UYKCh. 4.4 - Prob. 65UYKCh. 4.4 - Prob. 66UYKCh. 4.4 - Prob. 67UYKCh. 4.4 - Prob. 68ECh. 4.4 - Prob. 69ECh. 4.4 - Prob. 70ECh. 4.4 - Prob. 71ECh. 4.4 - Prob. 72ECh. 4.4 - Prob. 73ECh. 4.4 - Prob. 74ECh. 4.4 - Prob. 75ECh. 4.4 - Prob. 76ECh. 4.4 - Prob. 77ECh. 4.4 - Prob. 78ECh. 4.4 - Prob. 79ECh. 4.4 - Prob. 80ECh. 4.4 - Prob. 81ECh. 4.4 - Prob. 82ECh. 4.4 - Prob. 83ECh. 4.4 - Prob. 84ECh. 4.4 - Prob. 85ECh. 4.4 - Prob. 86ECh. 4.4 - Prob. 87ECh. 4.4 - Prob. 88ECh. 4.5 - Prob. 89UYKCh. 4.5 - Prob. 90UYKCh. 4.5 - Prob. 91UYKCh. 4.5 - Prob. 92UYKCh. 4.5 - Prob. 93UYKCh. 4.5 - Prob. 94UYKCh. 4.5 - Prob. 95UYKCh. 4.5 - Prob. 96ECh. 4.5 - Prob. 97ECh. 4.5 - Prob. 98ECh. 4.5 - Prob. 99ECh. 4.5 - Prob. 100ECh. 4.5 - Prob. 101ECh. 4.5 - Prob. 102ECh. 4.5 - Prob. 103ECh. 4.5 - Prob. 104ECh. 4.5 - Prob. 105ECh. 4.5 - Prob. 106ECh. 4.5 - Prob. 107ECh. 4.5 - Prob. 108ECh. 4.5 - Prob. 109ECh. 4.5 - Prob. 110ECh. 4.5 - Prob. 111ECh. 4.5 - Prob. 112ECh. 4.5 - Prob. 113ECh. 4.5 - Prob. 114ECh. 4.5 - Prob. 115ECh. 4.5 - Prob. 116ECh. 4.5 - Prob. 117ECh. 4.5 - Prob. 118ECh. 4.5 - Prob. 119ECh. 4.5 - Prob. 120ECh. 4.5 - Prob. 121ECh. 4.5 - Prob. 122ECh. 4.5 - Prob. 123ECh. 4 - Prob. 124ECh. 4 - Prob. 125ECh. 4 - Prob. 126ECh. 4 - Prob. 127ECh. 4 - Prob. 128ECh. 4 - Prob. 129ECh. 4 - Prob. 130ECh. 4 - Prob. 131ECh. 4 - Prob. 132ECh. 4 - Prob. 133ECh. 4 - Prob. 134ECh. 4 - Prob. 135ECh. 4 - Prob. 136ECh. 4 - Prob. 137ECh. 4 - Prob. 138ECh. 4 - Prob. 139E
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