Problem Set 1 Lind Chapter 9

Topics: Mean, Median, Arithmetic mean Pages: 6 (1251 words) Published: April 4, 2009
Problem Set I

Complete and submit the following problem set:  
Lind Chapter 3: Exercises 60, 62, 68, 70, 72b.
Exercise 60: Owens Orchards sells apples in a large bag by weight. A sample of seven bags contained the following numbers of apples: 23, 19, 26, 17, 21, 24, 22. a. Compute the mean number and median number of apples in a bag. 17 26

19 24
21 23
22 22 [pic]median 22
23 21
24 19
26 17
b. Verify that _(X _ ) _ 0 = 26 17 Verify that ∑(X-¯X) = 0 (26-22) + (24-22) + (23-22) + (22-22) + (21-22) + (22-19) + (17-22) = 4 + 2 + 1 + 0 ' 1 ' 3 ' 5 = -0.2 Exercise 62: The Citizens Banking Company is studying the number of times the ATM located in a Loblaws Supermarket at the foot of Market Street is used per day. Following are the numbers of times the machine was used over each of the last 30 days. Determine the mean number of times the machine was used per day. 83 64 84 76 84 54 75 59 70 61

63 80 84 73 68 52 65 90 52 77
95 36 78 61 59 84 95 47 87 60
A. Determine the mean number of times the machine was used per day: Where n = 30
¯X = ?
¯X = ΣX/n
¯X = (83+64+84+76+84+54+75+59+70+61+63+80+84+73+68+52+65+90+52+77+95+36+78+61+59+84+95+47+87+60)/30 ¯X = 2,116/30
¯X = 70.53
Exercise 68: The American Automobile Association checks the prices of gasoline before many holiday weekends. Listed below are the self-service prices for a sample of 15 retail outlets during the May 2003 Memorial Day weekend in the Detroit, Michigan, area. 1.44 1.42 1.35 1.39 1.49 1.49 1.41 1.46

1.41 1.49 1.45 1.48 1.39 1.46 1.44
Where: N = 15
μ = ?
a. What is the arithmetic mean selling price?
μ= ΣX/N
μ = 1.44
b. What is the median selling price?
Higher to lower Lower to higher
1.49 1.35
1.49 1.39
1.49 1.39
1.48 1.41
1.46 1.41
1.45 1.42
1.45 1.44
1.44 1.44 [pic]Median 1.44
1.44 1.45
1.42 1.45
1.41 1.46
1.41 1.48
1.39 1.49
1.39 1.49
1.35 1.49
c. What is the modal selling price?
The modal selling price = 1.49
1.49
1.49
1.49
1.48
1.46
1.45
1.45
1.44
1.44
1.42
1.41
1.41
1.39
1.39
1.35
Exercise 70: A recent article suggested that if you earn $25,000 a year today and the inflation rate continues at 3 percent per year, you’ll need to make $33,598 in 10 years to have the same buying power. You would need to make $44,771 if the inflation rate jumped to 6 percent. Confirm that these statements are accurate by finding the geometric mean rate of increase. a) Compute the Range. Where: X= 38

¯X = 7.6
n = 5
MD |┤| =?
S^2 = ?
Solution 9
Range = large value ? smallest value
R= 12-3
R = 9
b) Compute the mean deviation. Solution 2.75
MD= Σ |(X-¯X)/n|
¯X=ΣX/n
= (12+6+7+3+10)/5
=38/5
¯X=7.6
Weigh of boxes send by UPS (X- ¯X) absolute deviation
12 (12-7.6) = 4.4 4.4
6 (6-7.6) = -1.6 1.6
7 (7-7.6) = -.76 .76
3 (3-7.6) = -4.6 4.6
10 (10-7.6) = 2.4 2.4
Total = 13.76
MD= Σ |(X-¯X)/n|
= 13.76/5
MD=2.75
c) Compute the standard deviation.
S^2= √(Σ ((X- [pic]X) [pic]^2)/(n-1))
Weight of boxes (X- ¯X) (X- [pic]¯X) [pic]2
12 (12-7.6) = 4.4 19.36
6 (6-7.6) = -1.6 2.56
7 (7-7.6) = -.76 .36
3 (3-7.6) = -4.6 21.16
10 (10-7.6) = 2.4 5.76
Total = 38 Total = 0 Total = 49.2
¯X=ΣX/n
= (12+6+7+3+10)/5
=38/5
¯X=7.6
S^2= √(Σ (([pic]38-7.6) ? ^2)/(5-1))
= (([pic]38-7.6) ? ^2)/(5-1)
= 49.2/(5-1)
=√12.3
[pic]S ? ^(2 )=3.5
Lind Chapter 5: Exercises 8, 66
Exercise 8: A sample of 2,000 licensed drivers revealed the following number of speeding violations. Number of Violations Number of Drivers:
 0 1,910
 1 46
 2 18
 3 12
 4 9
 5 or more 5
Total 2,000
a. What is the experiment?
A sample of 2,000 licensed drivers revealed the following number of speeding violations. 2,000 licensed drivers reviled speeding violation

b. List one possible event.
9 drivers and 4 violations

c. What is the probability that a particular driver...
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