Section 11.5  Conditional Probability

3.      
5.     

Use the following table for Problems 7  10 
	Full-time	Part-time	Unemployed	Totals	
0 - 17	24	164	371	559	
18 - 25	185	203	148	536	
26 - 34	348	67	27	442	
35 - 49	581	179	104	864	
50+	443	162	173	778	
Totals	1581	775	823	3179	

7. P(Part-time | 35  49 ) = 

9. P(Unemployed | 18  49) = 

Use the following table for Problems 11  14 
	Sony
PS 2	MS
Xbox	Nintendo
GameCube	Sega
Dreamcast	
Totals	
0 - 12	63	84	55	51	253	
13 - 18	105	139	92	113	449	
19 - 24	248	217	83	169	717	
25+	191	166	88	136	581	
Totals	607	606	318	469	2000	

11. P(Sony PS 2) = 

13. P(Nintendo GameCube | 13  24) = 

15. Let A = Sum of dice is 8, and B = Sum of dice is even.  Then
	A = {26, 35, 44, 53, 62}, and
	B = {11, 13, 15, 22, 24, 26, 
         31, 33, 35, 42, 44, 46, 
         51, 53, 55, 62, 64, 66}
P(A | B) = 

17. Let A = Doubles are rolled, and B = Sum of dice is less than 7.  Then
	A = {11, 22, 33},  (Note that not all doubles are counted, since B is smaller)
and	B = {11, 12, 13, 14, 15, 21, 22, 23, 24, 31, 32, 33, 41, 42, 51}
P(A | B) = 

Section 12.1  Measures of Central Tendency

1. Reorder the given data as: 2, 5, 7, 7, and 14.
	Mean = 7,	Median = 7,		Mode = 7
3. Reorder the given data as: 2, 5, 8, 11, 17, 39, 42, and 52.
	Mean = 22,	Median = 14,		Mode = No Mode
5. Reorder the given data as: 2.1, 3.4, 4.6, 5.6, 8.0, 8.2, 9.4, 12.2, 56.1, and 78.2.
	Mean = 18.78,	Median = 8.1,		Mode = No Mode
7. Reorder the given data as: 145, 178, 178, 188, 192, 201, 202, and 255.
	Mean = 192.375,	Median = 190,		Mode = 178
9. Reorder the given data as: 12, 8, 5, 5, 3, 0, 4, 9, and 21.
	Mean = 1/9 = 0.1111…  0.11,	Median = 3,		Mode = 5

13. Reorder the given data as:
22, 25, 26, 26, 29, 31, 31, 32, 33, 33, 33, 33, 33, 34, 34, 
35, 35, 35, 37, 38, 39, 39, 41, 41, 42, 44, 44, 49, 49, 74, 61, 80
	Mean = 38.71875,	Median = 35,		Mode = 33
17.	We may summarize the given data as:
	Weight	Scores	
Tests	2	85, 75, 90	
Quizzes	1	96, 88, 60, 76	
Final Exam	2(2) = 4	85	

Weighted Mean = 

21. Weighted Mean = 

23. Mean = 

25. Mean = 

Section 12.2  Measures of Dispersion

1. Range = 63F  (21F) = 63F  (21F) = 84F

3. Given the data set (in order): 1, 2, 5, 7, 8, 19, 22
Range = 22  (1) = 20
Using the Procedure for computing a Standard Deviation,

1. Determine the mean of the n numbers.

2. For each number, calculate the deviation (difference) between the number and the mean of the numbers.
Number	Mean	Number  Mean	
1	9.142857143	1  9.142857143 = 8.142857143	
2	9.142857143	2  9.142857143 = 7.142857143	
5	9.142857143	5  9.142857143 = 4.142857143	
7	9.142857143	7  9.142857143 = 2.142857143	
8	9.142857143	8  9.142857143 = 1.142857143	
19	9.142857143	19  9.142857143 = 9.857142857	
22	9.142857143	22  9.142857143 = 12.85714286	

3. Calculate the square root of each of the deviations and find the sum of these squared deviations.

Number	Number  Mean	(Number  Mean)2	
1	8.142857143	(8.142857143)2 = 66.30612245	
2	7.142857143	(7.142857143) 2 = 51.02040817	
5	4.142857143	(4.142857143) 2 = 17.16326531	
7	2.142857143	(2.142857143) 2 = 4.591836735	
8	1.142857143	(1.142857143) 2 = 1.306122449	
19	9.857142857	(9.857142857) 2 = 97.1632653	
22	12.85714286	(12.85714286) 2 = 165.3061224	
	Sum of Squares	402.8571429	

4. If the data is a population, then divide the sum by n. If the data is a sample, then divide the sum by n  1.  (Note the result from this step is the Variance)
Since the data given is a sample, we divide the sum of squares from step 3 by n  1.
n  1 = 7  1 = 6
Variance = 402.8571429/6  402.86/6 = 67.14 (Round the numerator to the nearest hundredth)

5. Find the square root of the quotient from Step 4.  (Note the result from this step is the Standard Deviation)
Standard Deviation = 

5. Given the data set (in order): 1.5, 1.9, 2.1, 3.0, 4.8

Range = 4.8  (1.5) = 3.3
Using the Procedure for computing a Standard Deviation,
1. Determine the mean of the n numbers.

2. For each number, calculate the deviation (difference) between the number and the mean of the numbers.
3. Calculate the square root of each of the deviations and find the sum of these squared deviations.

Number	Mean	Number  Mean	(Number  Mean)2	
1	2.66	1.5  2.66 = 1.16	(1.16)2 = 1.3456	
2	2.66	1.9  2.66 = 0.76	(0.76)2 = 0.5776	
5	2.66	2.1  2.66 = 0.56	( 0.56)2 = 0.3136	
7	2.66	3.0  2.66 =   0.34	(0.34)2 = 0.1156	
8	2.66	4.8  2.66 =   2.14	(2.14)2 = 4.5796	
		Sum of Squares	6.932	

4. If the data is a population, then divide the sum by n. If the data is a sample, then divide the sum by n  1.  (Note the result from this step is the Variance)
Since the data given is a sample, we divide the sum of squares from step 3 by n  1.
n  1 = 5  1 = 4
Variance = 6.932/4  6.93/4 = 1.73 (Round the numerator to the nearest hundredth)

5. Find the square root of the quotient from Step 4.  (Note the result from this step is the Standard Deviation)
Standard Deviation = 

7. Given the data set (in order): 48, 59, 68, 81, 87, 91, 92, 93, 100

Range = 100  48 = 52
Using the Procedure for computing a Standard Deviation,
1. Determine the mean of the n numbers.
 
2. For each number, calculate the deviation (difference) between the number and the mean of the numbers.
3. Calculate the square root of each of the deviations and find the sum of these squared deviations.
Number	Mean	Number  Mean	(Number  Mean)2	
48	79.89	48  79.89 = 1.16	(31.89)2 = 1016.9721	
59	79.89	59  79.89 = 0.76	(20.89)2 = 436.3921	
68	79.89	68  79.89 = 0.56	( 11.89)2 = 141.3721	
81	79.89	81  79.89 =   0.34	(1.11)2 = 1.2321	
87	79.89	87  79.89 =   2.14	(7.11)2 = 50.5521	
91	79.89	91  79.89 =   2.14	(11.11)2 = 123.4321	
92	79.89	92  79.89 =   2.14	(12.11)2 = 146.6521	
93	79.89	93  79.89 =   2.14	(13.11)2 = 171.8721	
100	79.89	100  79.89 =   2.14	(20.11)2 = 404.4121	
		Sum of Squares	2492.8889	

4. If the data is a population, then divide the sum by n. If the data is a sample, then divide the sum by n  1.  (Note the result from this step is the Variance)
Since the data given is a sample, we divide the sum of squares from step 3 by n  1.
n  1 = 9  1 = 8
Variance = 2492.8889/8 = 311.611125  311.61 (Round the numerator to the nearest hundredth)

5. Find the square root of the quotient from Step 4.  (Note the result from this step is the Standard Deviation)
Standard Deviation = 
9. Given the data set (in order): 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Range = 4  (4) = 0
Using the Procedure for computing a Standard Deviation,
1. Determine the mean of the n numbers.

2. For each number, calculate the deviation (difference) between the number and the mean of the numbers.
3. Calculate the square root of each of the deviations and find the sum of these squared deviations.

Number	Mean	Number  Mean	(Number  Mean)2	
4	4	4  4 = 0	(0)2 = 0	
4	4	4  4 = 0	(0)2 = 0	
4	4	4  4 = 0	(0)2 = 0	
…	…	…	…	
4	4	4  4 = 0	(0)2 = 0	
		Sum of Squares	0	

4. If the data is a population, then divide the sum by n. If the data is a sample, then divide the sum by n  1.  (Note the result from this step is the Variance)
Since the data given is a sample, we divide the sum of squares from step 3 by n  1.
n  1 = 17  1 = 16
Variance = 0/16 = 0.00 (Round the numerator to the nearest hundredth)

5. Find the square root of the quotient from Step 4.  (Note the result from this step is the Standard Deviation)
Standard Deviation = 
11. Given the data set (in order): 12, 8, 5, 1, 4, 7, 11

, , , , 4, 7, 11

Range = 11  (12) = 11  12 = 23
Using the Procedure for computing a Standard Deviation,
1. Determine the mean of the n numbers.

2. For each number, calculate the deviation (difference) between the number and the mean of the numbers.
3. Calculate the square root of each of the deviations and find the sum of these squared deviations.

Number	Mean	Number  Mean	(Number  Mean)2	
12	0.57	12  (0.57) = 11.43	(11.43)2 = 130.6449	
8	0.57	8  (0.57) = 7.43	(7.43)2 = 55.2049	
5	0.57	5  (0.57) = 4.43	(4.43)2 = 19.6249	
1	0.57	1  (0.57) = 0.43	(0.43)2 = 0.1849	
4	0.57	4  (0.57) = 4.57	(4.57)2 = 20.8849	
7	0.57	7  (0.57) = 7.57	(7.57)2 = 57.3049	
11	0.57	11  (0.57) = 11.57	(11.57)2 = 133.8649	
		Sum of Squares	417.7143	

4. If the data is a population, then divide the sum by n. If the data is a sample, then divide the sum by n  1.  (Note the result from this step is the Variance)
Since the data given is a sample, we divide the sum of squares from step 3 by n  1.
n  1 = 7  1 = 6
Variance = 417.7143/6  69.62 (Round the numerator to the nearest hundredth)

5. Find the square root of the quotient from Step 4.  (Note the result from this step is the Standard Deviation)
Standard Deviation =