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Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

SOLUTIONS TO PROBLEMS IN CHAPTER 1: INTRODUCTION TO STATISTICS 1.1

Examples of data in business disciplines: accounting – revenue/sales, cost of goods, salary expense, depreciation, utility costs, taxes, equipment inventory, etc. finance - World bank bond rates, number of failed savings and loans companies, measured risk of common stocks, stock dividends, foreign exchange rate, liquidity rates for a single-family, etc. human resources - salaries, size of engineering staff, years experience, age of employees, years of education, etc. marketing - number of units sold, dollar sales volume, forecast sales, size of sales force, market share, measurement of consumer motivation, measurement of consumer frustration, measurement of brand preference, attitude measurement, measurement of consumer risk, etc. operations and supply chain management - the number, location, and network missions of suppliers, production facilities, distribution centers, warehouses, cross-docks, and customers; the quantity and location of inventory, including raw materials, work in process (WIP), and finished goods, etc. information systems - CPU time, size of memory, number of work stations, storage capacity, percent of professionals who are connected to a computer network, dollar assets of company computing, number of “hits” on the Internet, time spent on the Internet per day, percentage of people who use the Internet, retail dollars spent in e-commerce, etc. production - number of production runs per day, weight of a product; assembly time, number of defects per run, temperature in the plant, amount of inventory, turnaround time, etc. management - measurement of union participation, measurement of employer support, measurement of tendency to control, number of subordinates reporting to a manager, measurement of leadership style, etc.

1.2

Examples of data that can be gathered for decision-making purposes in business industries:

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

manufacturing - size of punched hole, number of rejects, amount of inventory, amount of production, number of production workers, etc. insurance - number of claims per month, average amount of life insurance per family head, life expectancy, cost of repairs for major auto collision, average medical costs incurred for a single female over 45 years of age, etc. travel - cost of airfare, number of miles traveled for ground transported vacations, number of nights away from home, size of traveling party, amount spent per day on vacation besides lodging, etc. retailing - inventory turnover ratio, sales volume, size of sales force, number of competitors within 2 miles of retail outlet, area of store, number of sales people, etc. communications - cost per minute, number of phones per office, miles of cable per customer headquarters, minutes per day of long distance usage, number of operators, time between calls, etc. computing - age of company hardware, cost of software, number of CAD/CAM stations, age of computer operators, measure to evaluate competing software packages, size of data base, etc. agriculture - number of farms per county, farm income, number of acres of corn per farm, wholesale price of a gallon of milk, number of livestock, grain storage capacity, etc. banking - size of deposit, number of failed banks, amount loaned to foreign banks, number of tellers per drive-in facility, average amount of withdrawal from automatic teller machine, federal reserve discount rate, etc. healthcare - number of patients per physician per day, average cost of hospital stay, average daily census of hospital, time spent waiting to see a physician, patient satisfaction, number of blood tests done per week. 1.3

Descriptive statistics in recorded music industry : 1)

RCA total sales of compact discs this week, number of artists under contract to a company at a given time.

total dollars spent on advertising last month to promote an album.

number of units produced in a day.

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

number of retail outlets selling the company's products.

Inferential statistics in recorded music industry : 1)

Measure the average amount spent per month on recorded music for a few consumers, then use that figure to infer the average amount for the population.

Determination of market share for rap music by using the proportion of a randomly selected sample of 500 purchasers of recorded music who purchased rap music.

Determination of top ten single records by sampling the number of requests at a few radio stations.

Estimation of the average length of a single recording by using the average length of a sample of records.

The difference between descriptive and inferential statistics lies mainly in the usage of the data. These descriptive examples all gather data from every item in the population about which the description is being made. For example, RCA measures the sales on all its compact discs for a week and reports the total. In each of the inferential statistics examples, a sample of the population is taken and the population value is estimated or inferred from the sample. For example, it may be practically impossible to determine the proportion of buyers who prefer rap music. However, a random sample of buyers can be contacted and interviewed for music preference. The results can be inferred to population market share. 1.4

Descriptive statistics in manufacturing batteries to make better decisions : 1)

total number of worker hours per plant per week - help management understand labor costs, work allocation, productivity, etc.

company sales volume of batteries in a year - help management decide if the product is profitable, how much to advertise in coming year and compare to costs to determine profitability.

total amount of sulfuric acid purchased per month for use in battery production. - can be used by management to study wasted inventory, scrap, etc.

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

total amount of defective and/or rejected units produced per day/week/month. - can be used by management to study wasted resources, need for labor training, redesign of assembly process, etc.

Inferential Statistics in manufacturing batteries to make decisions :

1.5

Take a sample of batteries and test them to determine the average shelf life - use the sample average to reach conclusions about all batteries of this type. Management can then make labeling and advertising claims. They can compare these figures to the shelflife of competing batteries.

Take a sample of battery consumers and determine how many batteries they purchase per year. Infer to the entire population management can use this information to estimate market potential and penetration.

Interview a random sample of production workers to determine attitude towards company management - management can use this survey results to ascertain employee morale and to direct efforts towards creating a more positive working environment which, hopefully, results in greater productivity.

Size of sale ($) per customer in men‟s formal wear. Either by taking a sample or using a census, management could compute the average sale in men‟s formal wear of a weekly period and compare the number to the same average taken a year ago or a month ago to determine if more is being purchased per customer. Other variables might include number of sales per hour, number of people entering the department per day, number of dress shirts sold per day, etc.

Number of employees working per day. This variable could indicate the day of the week (certain days have more or less sales), sales activity (how sales are doing overall), or even health of associates. Other variables might include percent of employees absent due to illness, average number of hours worked per week per employee, number of open positions, etc.

Inventory turnover rate. How fast are items in the store selling? Other variables might include reorder rate, percent of storage space utilized, number of stockouts per week, etc.

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

1.6

Number of customers that enter the store per hour. This figure will vary by day, time of day, and season. Comparing figures on this variable from period to period can give some indication of sales trends which can help drive human resource planning, etc. Other variables might include amount of time spent per customer in the store per visit, distance that customers travel to shop in the store, number of referrals that customers make to other people annually, etc.

Percentage of people paying with cash. Percentage of people using credit cards. These can be used to expedite pay systems, investigate employee theft, calculate surcharges associated with credit cards, etc. Other variables might include average time per checkout, average wait time in pay line, etc.

Size of bill or tab. This variable is the total amount in dollars spent by a patron per visit to the restaurant. The bill or tab could be for an individual or a group and would include both food and beverages if they are all included in the bill. Of course, the measurement would be in dollars. This information could be very useful for the manager or owner to know the average size of a bill both in projecting out total revenues over a period or as a baseline before a marketing effort to increase sales.

Percentage of Capacity Filled. This variable could be measured at various intervals, times, and days of the week. The measurement would be calculated by taking the number of patrons in the restaurant at any one time divided by the total number of seats in the restaurant (capacity). From this, management could make staffing decisions for various times and days of the week. In addition, management could make decisions about when to expand, how much to advertise, and/or when to run specials.

Length of Stay. The measurement is how many minutes people are actually in the restaurant from the time they are assigned a table until they are leaving. From this, management could determine customer turnover rates which have capacity implications. That is, how many times in a day is an average table “turned over”. If people stay longer, do they spend more?

Number of Arrivals per 5-minute intervals. The measurement is how many customers arrive at the front door to be greeted by the maître„d in any given five-minute period. This figure will likely vary by day of the week, season of the year, and time of day.

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

Management can use this information for staffing decisions and planning. 1.7

a) b) c) d) e) f) g) h)

ratio ratio ordinal nominal ordinal ratio nominal ratio

1.8

a) b) c) d) e) f) g) h)

ordinal ratio nominal ratio ratio ratio nominal ordinal

1.9

The population for this study is the 900 electric contractors who purchased Mapletech‟s wire.

The sample is the randomly chosen group of 35 contractors.

The statistic is the average satisfaction score for the sample of thirty-five contractors.

The parameter is the average satisfaction score for all 900 electric contractors in the population.

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

Legal Notice Copyright

Copyright © 2020 by John Wiley & Sons Canada, Ltd. or related companies. All rights reserved. The data contained in these files are protected by copyright. This manual is furnished under licence and may be used only in accordance with the terms of such licence. The material provided herein may not be downloaded, reproduced, stored in a retrieval system, modified, made available on a network, used to create derivative works, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise without the prior written permission of John Wiley & Sons Canada, Ltd.

SOLUTIONS TO PROBLEMS IN CHAPTER 2

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

Range = max-min = 29-(-12) = 41 Class width = 41/5 = 8.2 ≈ 9 The 5 class frequency distribution: Class Interval –15 - under –6 –6 - under 3 3 - under 12 12 - under 21 21 - under 30 Totals

Frequency 7 12 13 9 9 50

b) Class width = 41/10 = 4.1 ≈ 5. 10 class frequency distribution: Class Interval –15 - under –10 –10 - under –5 –5 - under 0 0 - under 5 5 - under 10 10 - under 15 15 - under 20 20 - under 25 25 - under 30 30 - under 35 Totals

Frequency 2 5 7 10 7 3 7 4 5 0 50

c) The ten class frequency distribution gives a more detailed breakdown of temperatures. It allows locating more accurately the temperatures with the greatest frequency. The class with the highest frequency (modal class), is 0 – under 5 class with a frequency of 10. The five class distribution collapses the intervals into broader classes making it appear that there are nearly equal frequencies in each class.

2.2 The range is 22 (61-39). We will use 8 classes. The class width will be 3. The frequency distribution is as shown below Class Interval

Frequency

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

39 - under 42 42 - under 45 45 - under 48 48 - under 51 51 - under 54 54 - under 57 57 - under 60 60 - under 63 Totals

3 5 20 21 26 11 11 3 100

The distribution reveals that 49 of the 100 boxes of raisins contain 51 or less raisin (39 under 51). It shows that there are three boxes that have 10 or more extra raisins (60 under 63) and three boxes that have 8-11 less raisins (39 – under 41) than the boxes are supposed to contain.

2.3 Class Cumulative Interval Frequency Frequency 0-5 6 5 - 10 8 10 - 15 17 15 - 20 23 20 - 25 18 25 - 30 10 30 - 35 4 TOTAL 86

Class

Relative

Midpoint

Frequency

2.5 7.5 12.5 17.5 22.5 27.5 32.5

6/86 = .0698 .0930 .1977 .2674 .2093 .1163 .0465 1.0000

6 14 31 54 72 82 86

The relative frequency tells us that it is most probable that a customer is in the 15 - 20 category (.2674). Over two thirds (.6744) of the customers are between 10 and 25 years of age.

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

2.4 Class

Class

Relative

Cumulative Interval

Frequency

Midpoint

Frequency

0-2 2-4 4-6 6-8 8-10 TOTAL

218 207 56 11 8 500

1 3 5 7 9

.436 .414 .112 .022 .016 1.000

Frequency

2.5

2.6

218 425 481 492 500

Some examples of cumulative frequencies in business: sales for the fiscal year, costs for the fiscal year, spending for the fiscal year, inventory build-up, accumulation of workers during a hiring buildup, production output over a time period.

Histogram:

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

Frequency Polygon:

Comment: The assembly times “pile up” near the middle of the graphs indicating that many of the assembly times are between 36 and 42 minutes.

2.7

Histogram:

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

Frequency Polygon:

Comment: The histogram indicates that the number of calls per shift varies widely. However, the heavy numbers of calls per shift fall in the 50 to 80 range. Since these numbers occur quite frequently, staffing planning should be done with these number of calls in mind realizing from the rest of the graph that there may be shifts with as few as 10 to 20 calls.

2.8 Ogive:

Cummulative Frequency

60 50 40 30 20 10 0 4.5

7.5

10.5

13.5

16.5

19.5

Midpoint

2.9

STEM

LEAF

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

21 22 23 24 25 26 27

2 8 8 9 0 1 2 4 6 6 7 9 9 0 0 4 5 8 8 9 9 9 9 0 0 3 6 9 9 9 0 3 4 5 5 7 7 8 9 0 1 1 2 3 3 5 6 0 1 3

The stem and leaf plot indicates that sales prices vary quite a bit within the range of $212,000 and $273,000. It is evident from the stem and leaf plot that there is a strong grouping of prices in the five price ranges from the $220‟s through the $260‟s.

2.10

STEM

LEAF 1 2 3 4 5 6 7 8

3, 6, 7, 7, 7, 9, 9, 9 0, 3, 3, 5, 7, 8, 9, 9 2, 3, 4, 5, 7, 8, 8 1, 4, 5, 6, 6, 7, 7, 8, 8, 9 0, 1, 2, 2, 7, 8, 9 0, 1, 4, 5, 6, 7, 9 0, 7 0

The stem and leaf plot shows that the numbers of passengers per flight were relatively evenly distributed between the high teens through the sixties. Rarely was there a flight with at least 70 passengers. The category of 40's contained the most flights (10). 2.11 The histogram shows that there is only one airport with more than 105 million passengers and from the given problem information, we know that that airport is Atlanta‟s Hartsfield-Jackson International Airport which has more than 105 million passengers. 40% (12) of the top 30 airports have between 65 and 75 million passengers. The next largest grouping is between 55 and 65 million passengers in which there are six airports. 2.12 We assume that the class endpoints (10, 20, 30, …) are indicated on the horizontal axis and the marks between them represent the class midpoints; the cumulative frequencies are marked on the vertical axis. The ogive shows that out of 200, 50 pots contain less than 10 legal king crabs. About 90 selected pots (45%) have fewer than 20 legal king crabs, and about 120 (60%) contain less than 30 legal king crabs. However, 180 pots (90%) have less than 80 legal king crabs.

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

2.13 Airlines

Number of passengers (in millions)

Delta

164.6

164.6/787.7= 0.209

United

140.4

0.178

Southwest

134.0

0.170

American

107.9

0.137

China Southern

86.5

0.110

Ryanair

79.6

0.101

Lufthansa

74.7

0.095

Totals

787.7

1.000

360

Proportion

Pie chart:

Degrees

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

Bar chart:

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

2.14 Firm

Revenue ($U.S. millions)

Pfizer

67,809

67,809/291,153=0.233

Novartis

53,324

0.183

Merck & Co.

45,987

0.158

Bayer

44,200

0.152

GlaxoSmithKline

42,813

0.147

Johnson and Johnson

37,020

0.127

Totals

291,153

1.000

360

Proportion

Degrees

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

Pie chart:

Bar chart:

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

Underwriting Firm RBC Capital Markets TD Securities CIBC World Markets National Bank Financial BMO Capital Markets Total

Total Amount ($million) 29,172 25,193 19,875

Percent 26.8 23.1 18.3

17,653 16,958 108,851

16.2 15.6 100.0

Bar chart:

Total Amount ($million) BMO Capital Markets National Bank Financial CIBC World Markets TD Securities RBC Capital Markets 0

5,000

10,000 15,000 20,000 25,000 30,000 35,000

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

Pie chart:

15.6 26.8 16.2

18.3

23.1

RBC Capital Markets

TD Secirities

CIBC World Markets

National Bank Financial

BMO Capital Markets

The proportion, sizes and color of the pie slices clearly shows that RBC Capital Markets raised the highest amount ($29,172 million, 26.8%) and BMO Capital Markets raised the lowest amount ($16,958 million, 15.8%). 2. 16 Destination

Revenue ($ millions)

Proportion Degrees

U.S.

1,697

0.7767

279.61

Mexico

269

0.1231

44.32

Japan

171

0.0783

28.19

South Korea

0.0128

4.61

Taiwan

0.0073

2.63

China

0.0018

0.65

Totals

2,185

1.0000

360.0

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

Pie Chart:

2.17

Complaint Busy Signal Too long a Wait Could not get through Got Disconnected Transferred to the Wrong Person Poor Connection Total

Number

% of Total

420 184 85 37 10 8 744

56.45 24.73 11.42 4.97 1.34 1.08 99.99

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

2.18

Generally speaking, the tendency is that less fish caught and used for industrial products when more fish is caught and used for human food.

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

2.19

Generally speaking, the tendency is that sales are higher when more money is spent on advertising.

2.20 It appears from the graph that as job satisfaction decreases, there is an increase in tardiness. Thus, there appears to be an inverse relationship between job satisfaction and tardiness. The scatter plot also shows that when employees are highly satisfied, the level of tardiness is low.

2.21 One-Way Commute Distance (in km) 0-3

4 - 10

More than 10

Total

Number of Annual

0-2

184

117

396

Non-vacation -Day

3-5

114

More than 5

Absences

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

Total

119

231

182

532

There is a slight tendency for there to be a few more absences as plant workers commute further distances. Say, 6.6% of those who commute more than 10 km had more than 5 non-vacation absent days, as compared to 2.5% and 3% for those who commute 0-3 km and 4-10 km respectively. Comparing workers who travel 4-10 km to those who travel 03 km, there is about a 2:1 ratio in all three cells (0-2, 3-5, more than 5 non-vacation day absences) indicating that for these two categories (0-3 and 4-10), number of absences is essentially independent of commute distance.

2.22 Level of Education High School only

University Degree

Total

Acceptable

Unacceptable

Total

Rating of Service

There is a tendency that the lower the level of education, the more acceptable is the service. First of all, according to the table, the numbers of customers with different level of education are almost the same (11 with “high school only” and 14 with “university degree”). It appears that a much higher proportion of high school level education customers rate the service as “acceptable” than as “unacceptable” (9 to 2 ratio or about 4.5 times as many). On the other hand, more of the university degree educated customers rated the service as “unacceptable” than as “acceptable” (8 to 6 ratio). In addition, 60% or 9 customers out of 15 who rate the service as “acceptable” have only high school education, and 80% or 8 customers out of 10 who rate the service as “unacceptable” are university degree level educated.

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

2.23 a.

Time Series plot of Year 1 Sales 9,500

Sales in Year 1

9,000 8,500 8,000 7,500 7,000 6,500 6,000

Month

This time-series plot for the year 1 shows up and down swings of sales until October with sales strongly increasing for November and December due to perhaps the holiday season. If true, we could be seeing possible seasonal effects of the holiday season followed by low sales in January.

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

Time Series Plot of Year 1 to Year 5 Sales 12,000 11,000

Sales

10,000 9,000 8,000 7,000 6,000

Month Year 1

Year 2

Year 3

Year 4

Year 5

When placed together on one time series plot, the graphs tend to show the same shape virtually every year. This underscores the notion that there is some seasonality in the data. Sales are down in January, April, June, and October. Sales are highest in December, increases every year from October through December, and then drops dramatically in January. c.

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

With all five years of data shown chronologically, it is apparent that there is a repeating seasonal cycle within each year. In addition, however, there is a general trend of increasing sales over the five years.

2.24

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

Time Series Plot of Coolsville 2310 2290

Exports

2270 2250 2230 2210 2190 2170 2150 1

Quarter

Examining the exports for Coolsville over these two years, there was an increase in exports from quarter 1 to quarter 2, followed by a decline in quarter 3 and 4 in year 1. In year 2, there was an increase in exports from quarter 1 to 2 followed by a decline in quarter 3 and other increase in quarter 4. Overall, there seems to be little or no trend in exports over time just a pattern of ups and downs. b.

Time Series Plot of City Exports over 8 Quarters 14,000 12,000

Exports

10,000 8,000 6,000 4,000 2,000 0 1

Quarter Coolsville

Genius Grove

Highland

Inner City

Metro City

New New York

Orbit City

Springfield

Many of the cities actually have relatively constant exports over these 8 quarters with few significant ups and downs. Metro City (second highest at the end) seems to be the most volatile of the cities in terms of exports. Genius Grove consistently has the highest exports. 2.25 Range = max-min = 57-18 = 39 Solutions Manual 1-27 Chapter 1 Copyright © 2020 John Wiley & Sons Canada, Ltd. Unauthorized copying, distribution, or transmission of this page is strictly prohibited.

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

Class width = 39/6 = 6.5 ≈ 7 Class Interval

Frequencies

16 - under 23 23 - under 30 30 - under 37 37 - under 44 44 - under 51 51 - under 58 TOTAL

6 9 4 4 4 3 30

2.26

2.27

Class Interval

Frequency

Midpoint

Rel. Freq.

Cum. Freq.

20 - under 25 25 - under 30 30 - under 35 35 - under 40 40 - under 45 45 - under 50

17 20 16 15 8 6

22.5 27.5 32.5 37.5 42.5 47.5

.207 .244 .195 .183 .098 .073

17 37 53 68 76 82

Class Interval

Frequencies

50 - under 60 60 - under 70 70 - under 80 80 - under 90 90 - under 100 TOTAL

13 27 43 31 9 123

Histogram:

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

Frequency Polygon:

Ogive:

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

2.28

STEM 28 29 30 31 32 33

2.29

LEAF 4, 6, 9 0, 4, 8 1, 6, 8, 9 1, 2, 4, 6, 7, 7 4, 4, 6

5 Label A B C D

Value 55 121 83 46

Proportion .180 .397 .272 .151

Degrees 65 143 98 54 TOTAL 1.000

305 360

Pie Chart:

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

2.30

Bar Graph: Category A B C D E

2.31

Problem

Frequency 7 12 14 5 19

Frequency

Percent of Total

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

1 2 3 4 5 6 7 8 9 10

673 29 108 379 73 564 12 402 54 202 2496

26.96 1.16 4.33 15.18 2.92 22.60 0.48 16.11 2.16 8.09

Pareto Chart:

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

0 0

2.33 Yellowknife Steel Company Range = max-min = 69-36 = 33 Class width = 33/8 = 4.125 ≈ 5 Class Interval 32 - under 37 37 - under 42 42 - under 47 47 - under 52 52 - under 57 57 - under 62 62 - under 67 67 - under 72 TOTAL

Frequency 1 4 12 11 14 5 2 1 50

The highest frequencies are between 42 and 57.

2.34 Class Cumulative Interval

Frequency

Class

Relative

Midpoint

Frequency

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

20 – 25 25 – 30 30 – 35 35 – 40 40 – 45 45 – 50 TOTAL

2.35

8 6 5 12 15 7 53

22.5 27.5 32.5 37.5 42.5 47.5

8/53 = .1509 .1132 .0943 .2264 .2830 .1321 .9999

8 14 19 31 46 53

Frequency Distribution: Class Interval 10 - under 20 20 - under 30 30 - under 40 40 - under 50 50 - under 60 60 - under 70 70 - under 80 80 - under 90

Frequency 2 3 9 7 12 9 6 2 50

Histogram:

Frequency Polygon:

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

The normal distribution appears to peak near the center and diminish towards the end intervals.

2.36

a. Histogram and a Frequency Polygon for Problem 2.34 Class Interval 20 – 25 25 – 30 30 – 35 35 – 40 40 – 45 45 – 50 TOTAL

Frequency 8 6 5 12 15 7 53

Cumulative Frequency 8 14 19 31 46 53

Histogram:

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

Frequency Polygon:

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

b. Ogive:

Cumulative Frequency

50 40 30 20 10 0 22.5

27.5

32.5

37.5

42.5

47.5

Class Midpoint

2.37 Asking Price

Frequency

Cumulative Frequency

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

$ 80,000 - under $ 100,000 $ 100,000 - under $ 120,000 $ 120,000 - under $ 140,000 $ 140,000 - under $ 160,000 $ 160,000 - under $ 180,000 $ 180,000 - under $ 200,000

21 27 18 11 6 3 86

21 48 66 77 83 86

Histogram: 30

Frequency

0 90,000

110,000

130,000

150,000

170,000

190,000

Class Midpoints

Frequency Polygon:

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

Frequency

0 90,000

110,000

130,000

150,000

170,000

190,000

Class Midpoints

Ogive: 100

Frequencies

0 80,000

100,000

120,000

140,000

160,000

180,000

200,000

Class Endpoints

2.38

Stem and Leaf Plot: STEM 1 2 3

LEAF 2, 3, 6, 7, 8, 8, 8, 9, 9 0, 3, 4, 5, 6, 7, 8 0, 1, 2, 2

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

Comments: The stem and leaf plot shows that the travel times are relatively evenly spread out between 12 days and 32 days. It also shows that the most travel times fall in the 12 to 19 day interval followed by the 20 to 28 day interval. Only four of the travel times were thirty or more days; 18 days is the most frequently occurring travel time (occurred three times).

2.39 Price

Frequency

$1.75 - under $1.90 $1.90 - under $2.05 $2.05 - under $2.20 $2.20 - under $2.35 $2.35 - under $2.50 $2.50 - under $2.65 $2.65 - under $2.80

9 14 17 16 18 8 5 87

Cumulative Frequency 9 23 40 56 74 82 87

Histogram:

Frequency Polygon:

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

Ogive:

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

2.40

Genre R&B Alternative Rap Country Soundtrack Metal Classical Latin TOTAL

Albums Sold 146.4 102.6 73.7 64.5 56.4 26.6 14.8 14.5

Proportion .29 .21 .15 .13 .11 .05 .03 .03 1.00

Degrees 104.4 75.6 54.0 46.8 39.6 18.0 10.8 10.8 360.0

Pie Chart:

Classical 3% Latin 3% Metal 5%

R&B 29% Soundtrack 11% Country 13%

Rap 15%

Alternative 21%

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

2.41

The higher is the exchange rate more Canadian travellers go to the U.S. and less the U.S. travellers do to Canada. Solutions Manual 1-43 Chapter 1 Copyright © 2020 John Wiley & Sons Canada, Ltd. Unauthorized copying, distribution, or transmission of this page is strictly prohibited.

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

2.42 Industrial Source

Total Emissions (tonnes)

Proportion

Degrees

Upstream petroleum

1,637,651

0.430

154.6

Aluminum

496,103

0.130

46.8

Wood

385,909

0.101

36.4

Nonferrous smelting and refining

354,907

0.093

33.5

Mining and rock quarrying

312,598

0.082

29.5

Pulp and paper

193,447

0.051

18.3

Downstream petroleum

145,192

0.038

13.7

Cement and concrete

128,856

0.034

12.2

Chemicals

82,202

0.022

7.8

Grain

75,632

0.020

7.1

Totals

3,812,497

1.0000

360.0

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

2.43 The Pareto chart indicates that fault in raw material causes 44.2% of the defects and becomes the major problem. According to the chart, 23.4% of the bottles were rejected because of incorrect thickness which can be identified as the second severe problem. The steepest slopes correspond to “fault in raw material”, “thickness”, and “broken handle” categories. They represent 84.8% causes of poor-quality bottles.

Solution Manual for Black, Bayley, Castillo: Business Statistics, Third Canadian Edition

2.44

STEM 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59

LEAF 12, 16, 24, 32, 99, 99 04, 28, 39, 46, 61, 88 20, 40, 59 12 53, 54 30, 34, 58 22, 34, 66, 78 63 48, 49, 90 66 21, 54, 57, 63, 91 38, 66, 66 31, 78 56 69 37, 50 31, 32, 58, 73 19, 23

2.45 STEM

LEAF

00, 68