Part -1:
1. A chain of sport shops catering to beginning skiers, headquartered in Aspen, Colorado, plans to conduct a study of how much a beginning skier spends on his or her initial purchase of equipment and supplies. Based on these figures, it wants to explore the possibility of offering combinations, such as a pair of boots and a pair of skis, to induce customers to buy more. A sample of cash register receipts revealed these initial purchases:
|
$143
|
$84
|
$139
|
$161
|
$175
|
$84
|
$126
|
$149
|
$140
|
|
127
|
263
|
232
|
132
|
172
|
149
|
170
|
215
|
105
|
|
220
|
126
|
90
|
171
|
162
|
229
|
121
|
116
|
149
|
|
126
|
144
|
118
|
172
|
156
|
215
|
87
|
172
|
230
|
|
162
|
195
|
128
|
126
|
142
|
118
|
127
|
144
|
|
(a) Find the smallest class interval. Use five classes.(Round your answer to 1 decimal place. Omit the "Consider the following chartquot; sign in your response.)
(b) What would be a better class interval? (Omit the "Consider the following chartquot; sign in your response.)
(c) Organize the data into a frequency distribution using a lower limit of $80.
2. The number of families who used the Minneapolis YWCA day care service was recorded over a 30-day period. The results are as follows:
|
60
|
46
|
64
|
43
|
70
|
46
|
44
|
39
|
53
|
53
|
|
41
|
41
|
65
|
33
|
3
|
20
|
46
|
18
|
44
|
17
|
|
57
|
26
|
5
|
67
|
47
|
22
|
16
|
7
|
39
|
48
|
(a) Construct a cumulative frequency distribution of this data.
(b) Select a graph of the cumulative frequency polygon of the given data.
(c) How many days saw fewer than 30 families utilize the day care center?
(d) The highest 60 percent of the days had at least families.
3. JetBlue Airways is an American low-cost airline headquartered in New York City. Its main base is John F. Kennedy International Airport. JetBlue's revenue in 2001 was $621.4 million. By 2009, revenue had increased to $3,124.5 million.
What was the geometric mean annual increase for the period? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)
Consider the following chart
(a) What is this chart called?
(b) How many observations are in the study?
(c) What are the maximum and the minimum values?
(d) Around what values do the observations tend to cluster?
4. The first row of a stem-and-leaf chart appears as follows: 62 | 1 3 3 7 9. Assume whole number values. (The stem represents the ten's position and the leaf represents the one's position.)
(a) What is the "possible range" of the values in this row?
(b) How many data values are in this row?
(c) Select the actual values in this row of data.
621 623 623 627 629
621 623 627 623 629
621 627 623 623 629
623 621 623 629 627
5. In a study of the gasoline mileage of model year 2011 automobiles, the mean miles per gallon was 27.5 and the median was 26.8. The smallest value in the study was 12.70 miles per gallon, and the largest was 50.20. The first and third quartiles were 17.95 and 35.45 miles per gallon, respectively.
Determine the type of skewness.
Positively skewed
Negatively skewed
6. Silver Springs Moving and Storage, Inc., is studying the relationship between the number of rooms in a move and the number of labor hours required for the move. As part of the analysis the CFO of Silver Springs developed the following scatter diagram.
(a) How many moves are in the sample?
(b) Choose the correct answer.
Labor hours increase as the number of rooms decrease
Labor hours increase as the number of rooms increase
Labor hours decrease as the number of rooms increase
7. Ski Resorts of Vermont, Inc., is considering a merger with Gulf Shores Beach Resorts, Inc., of Alabama. The board of directors surveyed 50 stockholders concerning their position on the merger. The results are reported below.
|
|
Opinion
|
|
|
|
|
|
|
Number of shares held
|
Favor
|
Opposed
|
Undecided
|
Total
|
|
Under 200
|
8
|
6
|
2
|
16
|
|
200 up to 1,000
|
6
|
8
|
1
|
15
|
|
Over 1,000
|
6
|
12
|
1
|
19
|
|
|
|
|
|
|
|
Total
|
20
|
26
|
4
|
50
|
(a) What level of measurement is used in this table?
(b) What is this table called?
(c) What group seems most strongly opposed to the merger?
8. The unemployment rate in the state of Alaska by month is given in the table below:
|
Jan
|
Feb
|
Mar
|
Apr
|
May
|
Jun
|
Jul
|
Aug
|
Sep
|
Oct
|
Nov
|
Dec
|
|
7.90
|
7.10
|
7.90
|
6.70
|
6.80
|
6.60
|
8.80
|
8.70
|
8.80
|
7.90
|
7.70
|
7.20
|
(a) What is the arithmetic mean of the Alaska unemployment rates? (Round your answer to 2 decimal places.)
(b) Find the median and the mode for the unemployment rates. (Round your answers to 2 decimal places.)
9. What is the level of measurement for each of the following variables?
a. Student IQ ratings.
b. Distance students travel to class.
c. The jersey numbers of a sorority soccer team.
d. A classification of students by state of birth.
e. A ranking of students as freshman, sophomore, junior, and senior.
f. Number of hours students study per week.
10. What type of variable is the number of gallons of gasoline pumped by a filling station during a day?
Qualitative
Continuous
Attribute
Discrete
11. What type of variable is the number of robberies reported in your city?
Attribute
Continuous
Quantitative
Qualitative
12. The following frequency distribution reports the number of frequent flier miles, reported in thousands, for employees of Brumley Statistical Consulting, Inc., during the first quarter of 2007.
|
Frequent
Flier Miles
(000)
|
Number of
Employees
|
|
0 up to 4
|
5
|
|
|
4 up to 8
|
13
|
|
|
8 up to 12
|
22
|
|
|
12 up to 16
|
8
|
|
|
16 up to 20
|
2
|
|
|
|
|
|
|
Total
|
50
|
|
(a) How many employees were studied?
(b) What is the midpoint of the first class? (Round your answer to 1 decimal place.)
(d) A frequency polygon is to be drawn. What are the coordinates of the plot for the first class?
13. When data is collected using a qualitative, nominal variable, what is true about a frequency distribution that summarizes the data?
Upper and lower class limits must be calculated.
A pie chart can be used to summarize the data.
Number of classes is equal to the number of variable's values plus 2.
The "5 to the k rule" can be applied.
14. A sample of the personnel files of eight employees at the Pawnee location of Acme Carpet Cleaners, Inc., revealed that during the last six-month period they lost the following number of days due to illness:
A sample of eight employees during the same period at the Chickpee location of Acme Carpets revealed they lost the following number of days due to illness.
(a) Calculate the range, mean and mean deviations for the Pawnee location and the Chickpee location. (Round mean and mean deviation to 2 decimal places.)
(b-1) Based on the sample data, which location has fewer lost days?
(b-2) Based on the sample data, which location has less variation?
Part -2:
1. A study of 204 advertising firms revealed their income after taxes:
|
Income after Taxes
|
Number of Firms
|
|
Under $1 million
|
104
|
|
$1 million to $20 million
|
54
|
|
$20 million or more
|
40
|
|
(a) What is the probability an advertising firm selected at random has under $1 million in income after taxes? (Round your answer to 2 decimal places.)
(b-1) What is the probability an advertising firm selected at random has either an income between $1 million and $20 million, or an income of $20 million or more? (Round your answer to 2 decimal places.)
(b-2) What rule of probability could be applied?
2. A student is taking two courses, history and math. The probability the student will pass the history course is .51, and the probability of passing the math course is .68. The probability of passing both is .42.
What is the probability of passing at least one? (Round your answer to 2 decimal places.)
3. Solve the following:
(a) 30!/26!
(b) 10P6 =
(c) 9C6 =
The following information applies to the questions displayed below.]
4. Joe Mauer of the Minnesota Twins had the highest batting average in the 2009 Major League Baseball season. His average was .482. So assume the probability of getting a hit is .482 for each time he batted. In a particular game, assume he batted five times.
( a) This is an example of what type of probability?
5. (b) What is the probability of getting five hits in a particular game? (Round your answer to 3 decimal places.)
Calculate probabilities using the rules of multiplication.
6. There are 29 families living in the Willbrook Farms Development. Of these families 17 prepared their own federal income taxes for last year, 7 had their taxes prepared by a local professional, and the remaining 5 by H&R Block.
(a) What is the probability of selecting a family that prepared their own taxes? (Round your answers to 3 decimal places.)
(b) What is the probability of selecting two families both of which prepared their own taxes?(Round your answers to 3 decimal places.)
(c) What is the probability of selecting three families, all of which prepared their own taxes? (Round your answers to 3 decimal places.)
(d) What is the probability of selecting two families, neither of which had their taxes prepared by H&R Block? (Round your answers to 3 decimal places.)
Define the term conditional probability.
7. Compute the mean and variance of the following probability distribution. (Round your answers to 2 decimal places.)
|
X
|
P(X)
|
|
2
|
.1
|
|
4
|
.20
|
|
6
|
.30
|
|
8
|
.40
|
| |
06-03 Compute the mean of a probability distribution.
06-04 Compute the variance and standard deviation of a probability distribution.
8. Suppose the Internal Revenue Service is studying the category of charitable contributions. A sample of 25 returns is selected from young couples between the ages of 20 and 35 who had an adjusted gross income of more than $100,000. Of these 25 returns 5 had charitable contributions of more than $1,000. Suppose 4 of these returns are selected for a comprehensive audit.
(a) You should use the hypergeometric distribution because
(b) What is the probability exactly one of the four audited had a charitable deduction of more than $1,000? (Round your answer to 4 decimal places.)
(c) What is the probability at least one of the audited returns had a charitable contribution of more than $1,000? (Round your answer to 4 decimal places.)
06-06 Describe and compute probabilities for a hypergeometric distribution.
9.An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of 3.8 emails per hour. Assume the arrival of these emails is approximated by the Poisson distribution.
(a) What is the probability Linda Lahey, company president, received exactly 4 emails between 4 P.M. and 5 P.M. yesterday? (Round your answer to 4 decimal places.)
(b) What is the probability she received 6 or more emails during the same period? (Round your answer to 4 decimal places.)
(c) What is the probability she received two or less emails during the period? (Round your answer to 4 decimal places.)
10. A recent CBS News survey reported that 75 percent of adults felt the U.S. Treasury should continue making pennies.
Suppose we select a sample of 10 adults.
(a-1) How many of the 10 would we expect to indicate that the Treasury should continue making pennies? (Round your answer to 2 decimal places.)
(a-2) What is the standard deviation? (Round your answer to 4 decimal places.)
(b) What is the likelihood that exactly 7 adults would indicate the Treasury should continue making pennies? (Round your answer to 4 decimal places.)
(c) What is the likelihood at least 7 adults would indicate the Treasury should continue making pennies? (Round your answer to 4 decimal places.)
Objective: 06-05 Describe and compute probabilities for a binomial distribution.
11. In a binomial situation, n = 5 and .25. Determine the probabilities of the following events using the binomial formula. (Round your answers to 4 decimal places.)
(a) x = 3
(b) x = 4
06-05 Describe and compute probabilities for a binomial distribution.
12. Refer to the following table.
|
First Event
|
|
|
|
|
|
|
Second Event
|
A1
|
A2
|
A3
|
Total
|
|
B1
|
3
|
4
|
5
|
12
|
|
B2
|
4
|
6
|
4
|
14
|
|
|
|
|
|
|
|
Total
|
7
|
10
|
9
|
26
|
|
|
|
|
|
|
| |
(a) Determine P(A1). (Round your answer to 2 decimal places.)
(b) Determine P(B1|A3). (Round your answer to 2 decimal places.)
(c) Determine P(B1 and A2). (Round your answer to 2 decimal places.)
05-07 Compute probabilities using a contingency table
13. The credit department of Lion's Department Store in Anaheim, California, reported that 20 percent of their sales are cash or check, 30 percent are paid with a credit card and 50 percent with a debit card. Twenty percent of the cash or check purchases, 80 percent of the credit card purchases, and 60 percent of the debit card purchases are for more than $50.
Ms. Tina Stevens just purchased a new dress that cost $120. What is the probability she paid cash or check? (Round your answer to 3 decimal places.)
05-08 Calculate probabilities using Bayes theorem.
14. 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.
06-02 Distinguish between a discrete and a continuous random variable.
A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month.
| Number of days absent |
Probability |
| 0 |
0.6 |
| 1 |
0.2 |
| 2 |
0.12 |
| 3 |
0.04 |
| 4 |
0.04 |
| 5 |
0 |
What is the variance of the number of days absent?
Compute the variance and standard deviation of a probability distribution.
Part - 3:
1. A study of 198 advertising firms revealed their income after taxes:
|
Income after Taxes
|
Number of Firms
|
|
Under $1 million
|
104
|
|
$1 million to $20 million
|
54
|
|
$20 million or more
|
40
|
| |
(a) What is the probability an advertising firm selected at random has under $1 million in income after taxes? (Round your answer to 2 decimal places.)
(b-1) What is the probability an advertising firm selected at random has either an income between $1 million and $20 million, or an income of $20 million or more? (Round your answer to 2 decimal places.)
(b-2) What rule of probability could be applied?
2. Refer to the following table.
|
First Event
|
|
|
|
|
|
|
Second Event
|
A1
|
A2
|
A3
|
Total
|
|
B1
|
2
|
2
|
3
|
7
|
|
B2
|
4
|
4
|
2
|
10
|
|
|
|
|
|
|
|
Total
|
6
|
6
|
5
|
17
|
|
|
|
|
|
|
| |
(a) Determine P(A3). (Round your answer to 2 decimal places.)
(b) Determine P(B2|A2). (Round your answer to 2 decimal places.)
(c) Determine P(B1 and A2). (Round your answer to 2 decimal places.)
3. All Seasons Plumbing has two service trucks that frequently need repair. If the probability the first truck is available is .80, the probability the second truck is available is .55, and the probability that both trucks are available is .40:
What is the probability neither truck is available? (Round your answer to 2 decimal places.)
4. The credit department of Lion's Department Store in Anaheim, California, reported that 22 percent of their sales are cash or check, 24 percent are paid with a credit card and 54 percent with a debit card. Twenty percent of the cash or check purchases, 80 percent of the credit card purchases, and 65 percent of the debit card purchases are for more than $50.
Ms. Tina Stevens just purchased a new dress that cost $120. What is the probability she paid cash or check? (Round your answer to 3 decimal places.)
5. Solve the following:
(a) 50!/46!
(b) 10P6 =
(c) 8C5 =
6. In a binomial distribution, and. Find the probabilities of the following events. (Round your answers to 4 decimal places.)
(a) Probability
(b) Probability
(c) Probability
7. In a Poisson distribution, . (Round your answers to 4 decimal places.)
(a) What is the probability that ?
Probability
(b) What is the probability that ?
Probability
8. Recent information published by the U.S. Environmental Protection Agency indicates that Honda is the manufacturer of four of the top ten vehicles in terms of fuel economy.
(a) Determine the probability distribution for the number of Hondas in a sample of three cars chosen from the top ten. (Round your answers to 3 decimal places.)
(b) What is the likelihood that in the sample of three at least one Honda is included? (Round your answer to 3 decimal places.)
9. The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 224 customers on the number of hours cars are parked and the amount they are charged.
|
Number of Hours
|
Frequency
|
Amount Charged
|
|
1
|
|
16
|
|
$
|
3
|
|
|
2
|
|
33
|
|
|
8
|
|
|
3
|
|
43
|
|
|
12
|
|
|
4
|
|
43
|
|
|
15
|
|
|
5
|
|
37
|
|
|
22
|
|
|
6
|
|
16
|
|
|
24
|
|
|
7
|
|
6
|
|
|
27
|
|
|
8
|
|
30
|
|
|
30
|
|
|
|
|
|
|
|
|
|
|
|
|
224
|
|
|
|
|
|
|
|
|
|
|
|
|
| |
(a) Convert the data on frequency into a distribution of probabilities. (Round your answers to 3 decimal places.)
|
Hours
|
Probability
|
|
1
|
|
|
2
|
|
|
3
|
|
|
4
|
|
|
5
|
|
|
6
|
|
|
7
|
|
|
8
|
|
| |
(b-1) Find the mean and the standard deviation of the number of hours parked. (Round your intermediate values and final answers to 3 decimal places.)
(b-2) How long is a typical customer parked? (Round your answer to 3 decimal places.)
The typical customer is parked for hours
(c) Find the mean and the standard deviation of the amount charged. (Round your intermediate values andfinal answers to 3 decimal places.)
A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 1, 2, 4, 6, 8, or 11 days last month.
|
Number of days absent
|
Probability
|
|
1
|
0.42
|
|
2
|
0.30
|
|
4
|
0.14
|
|
6
|
0.07
|
|
8
|
0.07
|
|
11
|
0
|
What is the variance of the number of days absent?
3.31
4.31
2.15
8.61