A Loblaws Supermarket At The Foot Of Market Street Case 8

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 had exactly two speeding violations?
Probability of an event (PE) = (Number of favorable outcomes)/(Total number of possible outcomes) PE = 18/2,000 = 0.009 d. What concept of probability does this illustrate? 100 male accounting/300 males in program=0.33 Exercise: 66: A survey of undergraduate students in the School of Business at Northern University revealed the following regarding the gender and majors of the students: Major Gender Accounting Management Finance Total Male 100 150 50 300 Female 100 50 50 200 Total 200 200 100 500 a. What is the probability of selecting a female student? 200 female / 500 total = 0.40 b. What is the probability of selecting finance or accounting major? 200 accounting + 100 Finance / 500 Total=0.60 c. What is the probability of selecting an accounting major, given that the person selected is a male? 100 male accounting / 300 males in program=0.33 Lind Chapter 6: Exercise 4 a, b, c. 4. a. Discrete random variables b. Continuous random variables c. Discrete Lind Chapter 7: Exercises 38, 44, 60 Exercise 38: The accounting department at Weston Materials, Inc., a national manufacturer of unattached garages, reports that it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normal distribution. a. Determine the z values for 29 and 34 hours. What percent of the garages take between 32 hours and 34 hours to erect? (29-32) / 2= z score= -1.5 (34-32) / 2=1.0 z score= 0.3413% of the garages will be complete between 32 and 34 hours. (32-32) / 2 = 0 (34-32) / 2 = 1 0.3513 = 34.13% b. What percent of the garages take between 29 hours and 34 hours to erect? (29-32) / 2 = -1.5 = 0.4332

(34-32) / 2 = 1 = 0.3413 0.4332 +0.3413 0.7745 = 77.45% c. What percent of the garages take 28.7 hours or less to erect? 28.7-32/2= -1.65 Z score for 1.65 = 0.4505 0.5000-.4505=0.0495% (used .5000 because its ½ of normal curve) Less than 5% is complete within 28.7 hours. d. Of the garages, 5 percent take how many hours or more to erect? (28.7-32) / 2 = -1.65 = 0.4505 =