# Basic Business Statistics : Frequency Distributions and Percentages (7 Problems)

19. The data displayed below represent monthly phone bills for a random sample of small business customers.

208 133 165 179 258 212 178 178

209 212 150 198 137 258 277 145

234 176 209 220 209 160 151 279

177 199 212 188 162 125 221 147

215 245 198 245 275 180 203 226

Which of the following would be the most appropriate class interval for displaying the data above in a frequency distribution with 5 intervals?

a. 40

b. 8

c. 35

d. 30

Please see attached for full question.

20. In an exit questionnaire 55 employees were asked to indicate a single major reason for leaving the company. Here are the results:

Reason given Number

Dissatisfaction with salary 15

Commute was too long 12

Dissatisfaction with supervisor 18

Dissatisfaction with benefits 10

What percent of employees were dissatisfied with either their salary

or their supervisor?

a. 33%

b. 55%

c. 60%

d. 58%

21. The results of a random sampling of bounced check fees is displayed

below:

Stem-and-Leaf Display

for Bounced Check Fee

Stem unit: 10

0 4 7 7 9 9

1 3 4 5 5 6 8

2 0 0 0 2 3 4 5 5 5 5 9 9 9

3 0 0 1 5 5 5 8 8

4 0 0 0 2 2 5 5 5

5 0 2 5 5

6 0 3 5

What percentage of the observed fees were more than $25?

a. 9%

b. 55%

c. 61%

d. 64%

22. The ordered array below represents the number of payoff demand

notices received by a mortgage company over a 25-day period.

11 12 13 13 14 15 16 16 16 17 18 19 21

22 22 24 25 27 27 29 31 32 33 33 42

If a cumulative relative frequency distribution for the number of

payoff demand notices received by the escrow company is

constructed with a first class of 10 but less than 15. What would be

the cumulative percentage of the 20 but less than 25 class?

a. 16%

b. 20%

c. 40%

d. 64%

23. The table below displays the opinions of a sample of college

students, broken down by gender, about a proposed bill to change

the tax structure for capital gains:

Female Male Totals

For 87 65 152

Neutral 25 14 39

Against 63 98 161

Totals 175 177 352

Referring to the table above, how many people are against the plan?

a. 63

b. 98

c. 161

d. 352

24. Referring to the table in #23 above, what percentage of the women

are neutral to the plan?

a. 7%

b. 14%

c. 25%

d. 64%

25. Referring to the table in #23 above, what percentage of the total

sample are in favor of the plan?

a. 18.47%

b. 43.18%

c. 49.72%

d. 50.28%

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#### Solution Summary

Seven problems relating to Frequency Distributions and Percentages are solved. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

Statistical problems from the book Basic Statistics for Business and Economics.

Lind, D. McGraw-Hill/Irwin Series

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.

b. Verify that _(X _ ) _ 0.

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

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

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.

72. The weights (in pounds) of a sample of five boxes being sent by UPS are: 12, 6, 7, 3, and 10.

a. Compute the range.

b. Compute the mean deviation.

c. Compute the standard deviation.

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?

b. List one possible event.

c. What is the probability that a particular driver had exactly two speeding violations?

d. What concept of probability does this illustrate?

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?

b. What is the probability of selecting a finance or accounting major?

c. What is the probability of selecting a female or an accounting major? Which rule of addition did you apply?

d. Are gender and major independent? Why?

e. What is the probability of selecting an accounting major, given that the person selected

is a male?

f. Suppose two students are selected randomly to attend a lunch with the president of the

University. What is the probability that both of those selected are accounting majors?

4. Which of these variables are discrete and which are continuous random variables?

a. The number of new accounts established by a salesperson in a year.

b. The time between customer arrivals to a bank ATM.

c. The number of customers in Big Nick's barber shop.

d. The amount of fuel in your car's gas tank.

e. The number of minorities on a jury.

f. The outside temperature today.

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?

b. What percent of the garages take between 29 hours and 34 hours to erect?

c. What percent of the garages take 28.7 hours or less to erect?

d. Of the garages, 5 percent take how many hours or more to erect?

44. The number of passengers on the Carnival Sensation during one-week cruises in the

Caribbean follows the normal distribution. The mean number of passengers per cruise is

1,820 and the standard deviation is 120.

a. What percent of the cruises will have between 1,820 and 1,970 passengers?

b. What percent of the cruises will have 1,970 passengers or more?

c. What percent of the cruises will have 1,600 or fewer passengers?

d. How many passengers are on the cruises with the fewest 25 percent of passengers?

60. In establishing warranties on HDTV sets, the manufacturer wants to set the limits so that few will need repair at manufacturer expense. On the other hand, the warranty period must be long enough to make the purchase attractive to the buyer. For a new HDTV the mean number of months until repairs are needed is 36.84 with a standard deviation of 3.34 months. Where should the warranty limits be set so that only 10 percent of the HDTVs need repairs at the manufacturer's expense?

12. The American Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 16 people reveals the mean yearly consumption to be 60 pounds with a standard deviation of 20 pounds.

a. What is the value of the population mean? What is the best estimate of this value?

b. Explain why we need to use the t distribution. What assumption do you need to make?

c. For a 90 percent confidence interval, what is the value of t?

d. Develop the 90 percent confidence interval for the population mean.

e. Would it be reasonable to conclude that the population mean is 63 pounds?

28. A processor of carrots cuts the green top off each carrot, washes the carrots, and inserts six to a package. Twenty packages are inserted in a box for shipment. To test the weight of the boxes, a few were checked. The mean weight was 20.4 pounds, the standard deviation 0.5 pounds. How many boxes must the processor sample to be 95 percent confident that the sample mean does not differ from the population mean by more than 0.2 pounds?

6. The MacBurger restaurant chain claims that the waiting time of customers for service is normally distributed, with a mean of 3 minutes and a standard deviation of 1 minute. The quality-assurance department found in a sample of 50 customers at the Warren Road

MacBurger that the mean waiting time was 2.75 minutes. At the .05 significance level, can we conclude that the mean waiting time is less than 3 minutes?

18. The management of White Industries is considering a new method of assembling its golf cart. The present method requires 42.3 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 24 carts, using the new method, was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes. Using the .10 level of significance, can we conclude that the assembly time using the new method is faster?

24. Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the afternoon shift than on the day shift. A sample of 54 day-shift workers showed that the mean number of units produced was 345, with a standard deviation of 21. A sample of 60 afternoon-shift workers showed that the mean number of units produced was 351, with a standard deviation of 28 units. At the .05 significance level, is the number of units produced on the afternoon shift larger?

38. Two boats, the Prada (Italy) and the Oracle (U.S.A.), are competing for a spot in the upcoming America's Cup race. They race over a part of the course several times. Below are the sample times in minutes. At the .05 significance level, can we conclude that there is a difference in their mean times?

Boat Times (minutes)

Prada (Italy) 12.9 12.5 11.0 13.3 11.2 11.4 11.6 12.3 14.2 11.3

Oracle (U.S.A.)14.1 14.1 14.2 17.4 15.8 16.7 16.1 13.3 13.4 13.6 10.8 19.0

30. There are four auto body shops in a community and all claim to promptly serve customers. To check if there is any difference in service, customers are randomly selected from each repair shop and their waiting times in days are recorded. The output from a statistical software package is:

Summary

Groups Count Sum Average Variance

Body Shop A 3 15.4 5.133333 0.323333

Body Shop B 4 32 8 1.433333

Body Shop C 5 25.2 5.04 0.748

Body Shop D 4 25.9 6.475 0.595833

12. For many years TV executives used the guideline that 30 percent of the audience were watching each of the prime-time networks and 10 percent were watching cable stations on a weekday night. A random sample of 500 viewers in the Tampa-St. Petersburg, Florida, area last Monday night showed that 165 homes were tuned in to the ABC affiliate, 140 to the CBS affiliate, 125 to the NBC affiliate, and the remainder were viewing a cable station. At the .05 significance level, can we conclude that the guideline is still reasonable?

26. A study regarding the relationship between age and the amount of pressure sales personnel feel in relation to their jobs revealed the following sample information. At the .01 significance level, is there a relationship between job pressure and age?

Degree of Job Pressure

Age (years) Low Medium High

Less than 25 20 18 22

25 up to 40 50 46 44

40 up to 60 58 63 59

60 and older 34 43 43