To assess the relationship between number of absences and grades, an instructor collects data from the ten students in a class and runs a simple regression. She finds a perfect negative relationship: as the number of absences goes up, grades go down. But then, the instructor remembers that there is an 11th person in the class: someone who never came to class but still managed somehow to get a perfect grade in the course. Conceptually (not mathematically) describe what will happen to the slope and correlation coefficient.
In: Statistics and Probability
An event organizing company runs four events a year, once every 3 months. They have 20 full time employees, which are needed for the events. Recently the operating costs have been considered too high. Which aggregate planning model would you propose for them? Justify the benefits of that system over other methods (5 points). Give five recommendations for reducing the operational costs for the company (5 points).
In: Operations Management
1, A police officer randomly selected 585 police records of larceny thefts. The accompanying data represent the number of offenses for various types of larceny thefts.
|
(a) |
Construct a probability model for type of larceny theft. |
|
(b) |
Are coin-operated machine larcenies unusual? |
|
(c) |
Are bicycle larcenies unusual? |
(a) Complete the table below.
| Type of Larceny Theft | Number of Offenses |
| Pocket picking | 9 |
| Purse snatching | 10 |
| Shoplifting | 124 |
| From motor vehicles | 222 |
| Motor vehicle accessories | 64 |
| Bicycles | 37 |
| From buildings | 108 |
| From coin-operated machines | 11 |
(Round to three decimal places as needed.)
2, A baseball player hit 61 home runs in a season. Of the 61 home runs, 17 went to right field,20 went to right center field, 12 went to center field, 11 went to left center field, and 1 went to left field.
|
(a) |
What is the probability that a randomly selected home run was hit to right field? |
|
(b) |
What is the probability that a randomly selected home run was hit to left field? |
|
(c) |
Was it unusual for this player to hit a home run to left field? Explain. |
(Round to three decimal places as needed.)
In: Statistics and Probability
A theme park owner records the number of times the same kids from two separate age groups ride the newest attraction.
| Age 13–16 | Time | Age 17–21 | Time |
|---|---|---|---|
| 1 | 11 | 1 | 5 |
| 2 | 8 | 2 | 3 |
| 3 | 3 | 3 | 7 |
| 4 | 1 | 4 | 4 |
| 5 | 9 | 5 | 9 |
| 6 | 2 | 6 | 1 |
| 7 | 7 | 7 | 3 |
| 8 | 8 | 8 | 5 |
| 9 | 6 | 9 | 5 |
| 10 | 6 | 10 | 1 |
Using the computational formula, what is the SS, sample variance, and standard deviation for the age group of 13–16? (Round your answers for variance and standard deviation to two decimal places.)
SS sample variance standard deviation
In: Math
A management facility divides workdays into 3 shifts – EarlyBird, Cricket and NightOwl. The facility recently hired 20 workers on the EarlyBird shift, 15 workers on the Cricket shift, and 10 workers on the NightOwl shift. Six of these workers are to be chosen for rigorous interviews. Suppose the selection is made in such a way that any particular group of six workers has the same chance of being selected as does any other group (that is, drawing choices without replacement).
In how many ways can all six interviewees come from the EarlyBird shift? What is the probability of that happening?
The facility manager is concerned that choosing 6 workers randomly might result in all interviewees coming from the same shift. Is this a valid concern? Explain.
How likely is it that interviewees come from at least 2 of the shifts?
The manager is concerned that at least one shift might not be represented. What is the
probability of that happening?
In: Statistics and Probability
The accompanying data include the total compensation (in $millions) for CEOs of 50 companies and the investment return for a recent year.
Company Compensation ($mil) Return
(%)
Company 1 20.6 17
Company 2 16.3 8
Company 3 27.8 10
Company 4 26.2 0
Company 5 31.2 15
Company 6 23.7 64
Company 7 15.1 54
Company 8 17.9 33
Company 9 11.9 13
Company 10 15.6 6
Company 11 17.9 34
Company 12 14.4 48
Company 13 12.7 21
Company 14 13.6 0
Company 15 14.9 59
Company 16 14.2 20
Company 17 13.4 4
Company 18 43.5 -20
Company 19 16.8 -8
Company 20 21.3 17
Company 21 14.5 3
Company 22 84.6 25
Company 23 24.1 7
Company 24 15.9 5
Company 25 22.9 25
Company 26 14.9 -1
Company 27 31.4 6
Company 28 14.6 27
Company 29 14.8 30
Company 30 60.3 39
Company 31 17.1 31
Company 32 17.9 -17
Company 33 19.2 24
Company 34 67.7 25
Company 35 12.7 33
Company 36 19.3 17
Company 37 18.1 5
Company 38 15.5 -5
Company 39 12.7 -19
Company 40 13.9 24
Company 41 19.4 5
Company 42 16.6 21
Company 43 17.2 0
Company 44 17.8 81
Company 45 61.1 24
Company 46 42.2 48
Company 47 14.9 36
Company 48 22.7 13
Company 49 39.8 -7
Company 50 16.8 -3
A. Compute the correlation coefficient between compensation and the investment return.
B. At the 0.05 level of significance, is the correlation between compensation and the investment return statistically significant?
- The null and alternative hypotheses
- The test statistic
- The p-value
C. Write a short summary of the findings in (a) and (b). Are the results surprising?
In: Statistics and Probability
Complete the hypothetical table below and explain in brief, the behavior of each type of cost.
|
Quantity |
Total Fixed Cost |
Total Variable Cost |
Total Cost |
Average Fixed Cost |
Average Variable Cost |
Average Total Cost |
Marginal Cost |
|
0 |
0 |
||||||
|
1 |
25 |
||||||
|
2 |
40 |
||||||
|
3 |
50 |
||||||
|
4 |
60 |
||||||
|
5 |
100 |
80 |
|||||
|
6 |
110 |
||||||
|
7 |
150 |
||||||
|
8 |
300 |
||||||
|
9 |
500 |
||||||
|
10 |
900 |
In: Economics
| Number | Face Value |
Percent Price |
Market Value |
Interest Rate |
$10 | Total | Annual |
| of Bonds | of | Commission | Bond | Interest | |||
| Purchased | Each Bond | per $1,000 bond | Investment | All Bonds | |||
| 50 | $1,000 | 85.00% | 8% | ||||
| 165 | $1,000 | 75.50% | 12.00% | ||||
| 30 | $1,000 | 92.25% | 10.75% | ||||
| 20 | $1,000 | 10.50% | 7% | ||||
| 25 | $1,000 | 71.50% | 9.90% | ||||
| 40 | $1,000 | 73.50% | 6.50% | ||||
| 80 | $1,000 | 80.25% | 4.80% | ||||
In: Finance
A study was conducted to investigate the influence of a driver's age, number of driving years and attention span (the higher, the more detailed) on the number of speeding tickets within the last five years. Given a driver at age 30, who has been driving for 10 years with an attention span score of 5, what is the number of tickets that can be expected? Data can be found in the tickets tab.
| 8 | 32 | 16 | 7 |
| 6 | 35 | 19 | 10 |
| 5 | 24 | 10 | 2 |
| 10 | 41 | 25 | 9 |
| 11 | 46 | 30 | 1 |
| 6 | 28 | 12 | 3 |
| 5 | 25 | 10 | 2 |
| 4 | 24 | 9 | 1 |
| 6 | 28 | 12 | 3 |
| 12 | 49 | 33 | 6 |
| 15 | 50 | 30 | 7 |
| 2 | 21 | 5 | 4 |
| 13 | 41 | 26 | 6 |
| 7 | 30 | 15 | 5 |
| 9 | 41 | 25 | 6 |
| 7 | 27 | 11 | 2 |
| 10 | 39 | 23 | 4 |
| 12 | 47 | 31 | 2 |
| 16 | 46 | 32 | 8 |
| 5 | 21 | 5 | 2 |
| 4 | 24 | 8 | 1 |
| 10 | 37 | 21 | 9 |
| 6 | 28 | 12 | 3 |
| 1 | 20 | 2 | 3 |
| 12 | 43 | 27 | 8 |
| 8 | 32 | 16 | 7 |
| 8 | 32 | 16 | 7 |
| 3 | 37 | 7 | 6 |
| 5 | 26 | 10 | 1 |
| 8 | 29 | 13 | 4 |
| 13 | 42 | 26 | 7 |
| 2 | 22 | 4 | 2 |
| 7 | 41 | 15 | 7 |
| 12 | 47 | 31 | 8 |
| 5 | 33 | 17 | 8 |
| 10 | 36 | 20 | 5 |
| 2 | 23 | 5 | 2 |
The obtained statistic is:
| .883 |
| .388 |
| 83.01 |
| 155.33 |
In: Statistics and Probability
LYFT enters into an agreement with University to set up a $60K prepaid account balance to be used for student rides from University sporting events. University pays at the beginning of each month and the balance is drawn down as trips are completed during the month. The contract runs from 7/1/2019 to 12/31/2019.
a. What entry(ies) does LYFT record on the first day of the month for this transaction? How does the entry change if LYFT receives the cash on the first day versus if receives the cash on the last day of the month?
B. Assuming LYFT aggregates and books the trips against University's balance at month-end, what entry is recorded at the end of the month if only $30K in rides are taken? What entry is recorded if the $20K unused balance is refunded to University at the end of the month?
c. If the contract is set up that any usage beyond the $50K will be billed to University at the end of the month, what entry(ies) would be recorded at month end if $75K in rides were taken during the period?
d. If LYFT grants all students enrolled at University a 10% discount, what would the entry(ies) be to record a $10 student ride from a University sporting event?
e. If the University does not pay for 6 months but utilizes $100K in rides, how would this be reflected in the 12/31/2019 balance sheet? What P&L considerations would you have to assess?
In: Accounting