A supermarket has determined that daily demand for one-liter milk bottles has an approximate bell shaped distribution, with a mean of 55 bottles and a variance of 36
a) How often can we expect between 43 and 67 bottles to be sold in a day? (Give a percentage.)
b) What percentage of the time will the number of bottles sold more than 61 bottles
c) If the supermarket begins each morning with a supply of 73 bottles how often will demand exceed the supply? (Give a percentage.)
In: Statistics and Probability
The weights of a certain dog breed are approximately normally
distributed with a mean of 49 pounds, and a standard deviation of
6.3 pounds. Answer the following questions. Write your answers in
percent form. Round your answers to the nearest tenth of a
percent.
a) Find the percentage of dogs of this breed that weigh less than
49 pounds. %
b) Find the percentage of dogs of this breed that weigh less than
46 pounds. %
c) Find the percentage of dogs of this breed that weigh more than
46 pounds. %
In: Statistics and Probability
The weight of an organ in adult males has a bell-shaped distribution with a mean of 310 grams and a standard deviation of 45 grams. Use the empirical rule to determine the following.
(a) About 68% of organs will be between what weights?
(b) What percentage of organs weighs between 220 grams and 400 grams?
(c) What percentage of organs weighs less than 220 grams or more than 400 grams?
(d) What percentage of organs weighs between 220 grams and 355 grams?
In: Statistics and Probability
The weights of a certain dog breed are approximately normally
distributed with a mean of 52 pounds, and a standard deviation of
6.7 pounds. Answer the following questions. Write your answers in
percent form. Round your answers to the nearest tenth of a
percent.
a) Find the percentage of dogs of this breed that weigh less than
52 pounds.
b) Find the percentage of dogs of this breed that weigh less than
47 pounds.
c) Find the percentage of dogs of this breed that weigh more than
47 pounds.
In: Statistics and Probability
A) Many celebrities and public figures have Twitter accounts with large numbers of followers. However, some of these followers are fake, resulting from accounts generated by spamming computers. In a sample of 46 twitter audits, the mean percentage of fake followers was ?̅= 15.9 with a standard deviation of ? = 9.3. Construct a 99% confidence interval for the mean percentage of fake Twitter followers.
B) An executive at Twitter claims that the percentage of fake Twitter followers is less than 10. Based on the confidence interval, is this a reasonable claim?
In: Statistics and Probability
Foreign direct investment includes portfolio investment. True False
Economic growth is measured as:
total output per year divided by the inflation rate.
the annual percentage change in real GDP.
total nominal GDP at the end of each year.
the percentage change in population growth per year.
the quarterly percentage change in nominal GDP.
According to the expenditures approach, gross domestic product represents the sum of consumption spending, government spending, net exports, and net investment.True False
In: Economics
The weight of an organ in adult males has a bell-shaped distribution with a mean of 310 grams and a standard deviation of 20 grams. Use the empirical rule to determine the following.
(a) About 95% of organs will be between what weights?
(b) What percentage of organs weighs between 250 grams and 370 grams?
(c) What percentage of organs weighs less than 250 grams or more than 370 grams?
(d) What percentage of organs weighs between 250 grams and 330 grams?
In: Math
Suppose that the mean retail price per gallon of regular grade gasoline in the United States is $3.45 with a standard deviation of $0.20 and that the retail price per gallon has a bell-shaped distribution. (a) What percentage of regular grade gasoline sold between $3.25 and $3.65 per gallon? % (b) What percentage of regular grade gasoline sold between $3.25 and $3.85 per gallon? % (c) What percentage of regular grade gasoline sold for more than $3.85 per gallon? %
In: Operations Management
A newly issued bond has a maturity of 10 years and pays a 7% coupon rate (with coupon payments coming once annually). The bond sells at par value.
a. What are the convexity and the duration of the bond? Use the formula for convexity in footnote 7. (Round your answers to 3 decimal places.)
| Convexity | |
| Duration |
b. Find the actual price of the bond assuming that its yield to maturity immediately increases from 7% to 8% (with maturity still 10 years). Assume a par value of 100. (Round your answer to 2 decimal places.)
| Actual Price of the Bond (%) |
c. What price would be predicted by the modified duration rule ΔPP=−D*Δy?ΔPP=−D*Δy? What is the percentage error of that rule? (Negative answers should be indicated by a minus sign. Round your answers to 2 decimal places.)
| Percentage Price change (%) | |
| Percentage Error (%) |
d. What price would be predicted by the modified
duration-with-convexity rule
ΔPP=−D*Δy+12×Convexity×(Δy)2?ΔPP=−D*Δy+12×Convexity×(Δy)2? What is
the percentage error of that rule? (Negative
answers should be indicated by a minus
sign. Round your answers to 2 decimal
places.)
| Percentage Price Change (%) | |
| Percentage Error (%) |
In: Finance
Use the following information for Delta Corporation to answer question 1:
|
Year |
20X1 |
20X2 |
|
Net sales |
$1,500,000 |
$1,656,598 |
|
Cost of goods sold |
675,000 |
745,469 |
|
Depreciation |
270,000 |
298,188 |
|
Interest paid |
43,600 |
44,000 |
|
Cash |
127,500 |
140,811 |
|
Accounts receivable |
450,000 |
496,980 |
|
Inventory |
525,000 |
579,809 |
|
Net fixed assets |
1,800,000 |
1,987,918 |
|
Accounts payable |
375,000 |
414,150 |
|
Notes payable |
45,000 |
50,000 |
|
Long-term debt |
500,000 |
500,000 |
|
Common stock |
1,000,000 |
1,000,000 |
|
Retained earnings |
982,500 |
1,241,368 |
|
Tax rate |
35% |
35% |
|
Dividend payout |
30% |
30% |
1. Delta has 600,000 common shares outstanding. The firm is projecting a 20% increase in net sales for the coming year (20X3). Delta uses the percentage of sales approach to plan for its financing needs. In using this approach, the firm assumes that cost of goods sold, all assets (current and fixed), and accounts payable will all remain a constant percentage of sales. Depreciation expense is assumed to be 15% of net fixed assets, while notes payable and long-term debt will remain at the same level as 20X2. The interest rate charged on notes payable and long-term debt is also expected to remain the same. The firm will aim to maintain its dividend payout of 30% for the foreseeable future.
a. Construct the pro-forma Statement of Comprehensive Income and Statement of Financial Position for Delta Corporation for 20X3. Calculate the external financing needed (EFN) for 20X3. Round all your numbers in the pro-forma statements to the nearest dollar.
b. Based on its 20X2 information, what is Delta’s capital intensity ratio? Round your answer to four decimal places.
c. What is Delta’s full capacity sales if it is currently operating at 80% capacity (20X2)? Round your answer to the nearest integer.
d. Recalculate the firm’s external financing needed (EFN) for 20X3 if Delta is only operating at 80% capacity. Assume that if the 20X3 net sales is lower than full capacity sales, then the net fixed assets in 20X3 will be the same as the net fixed assets in 20X2 (i.e., assume that the firm will purchase just enough fixed assets to cover depreciation expense for 20X3). Interpret this EFN number.
e. What is Delta’s internal growth rate for 20X2? Round your final answer in percentage to two decimal places.
f. What is Delta’s sustainable growth rate for 20X2? Round your final answer in percentage to two decimal places.
g. Assume that Delta is operating at 100% capacity. Calculate the EFN for the firm if it wants to grow its sales by 100% for 20X3. Interpret this EFN number.
In: Finance