Rocky Mountain National Park is a popular park for outdoor recreation activities in Colorado. According to U.S. National Park Service statistics, 46.7% of visitors to Rocky Mountain National Park in 2018 entered through the Beaver Meadows park entrance, 24.3% of visitors entered through the Fall River park entrance, 6.3% of visitors entered through the Grand Lake park entrance, and 22.7% of visitors had no recorded point of entry to the park.† Consider a random sample of 175 Rocky Mountain National Park visitors. Use the normal approximation of the binomial distribution to answer the following questions. (Round your answers to four decimal places.)
(a)
What is the probability that at least 65 visitors had a recorded
entry through the Beaver Meadows park entrance?
(b)
What is the probability that at least 60 but less than 70 visitors
had a recorded entry through the Beaver Meadows park entrance?
(c)
What is the probability that fewer than 11 visitors had a recorded
entry through the Grand Lake park entrance?
(d)
What is the probability that more than 40 visitors have no recorded
point of entry?
In: Statistics and Probability
Rocky Mountain National Park is a popular park for outdoor recreation activities in Colorado. According to U.S. National Park Service statistics, 46.7% of visitors to Rocky Mountain National Park in 2018 entered through the Beaver Meadows park entrance, 24.3% of visitors entered through the Fall River park entrance, 6.3% of visitors entered through the Grand Lake park entrance, and 22.7% of visitors had no recorded point of entry to the park.† Consider a random sample of 175 Rocky Mountain National Park visitors. Use the normal approximation of the binomial distribution to answer the following questions. (Round your answers to four decimal places.)
(a)
What is the probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance?
(b)
What is the probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance?
(c)
What is the probability that fewer than 11 visitors had a recorded entry through the Grand Lake park entrance?
(d)
What is the probability that more than 40 visitors have no recorded point of entry?
In: Statistics and Probability
A long segment of the suburban freeway is to be designed on level terrain. The level segment, however, is followed by a 4.5% grade, 2.0 miles in length. If the DDHV is 2,500 veh/h with 15% trucks (standard mix), how many lanes will be needed on the (a) upgrade, (b) downgrade, (c) level terrain segment to provide for the level of service C? Lane widths and lateral clearances may be assumed to be 12 ft and 6 ft, respectively. Ramp density is expected to be 1.0 ramps/mi. The PHF is 0.92. Good weather, no incidents, no work zones, and regular users of the facility may be assumed.
In: Civil Engineering
Q5. You are a theater owner fortunate to book a summer box office hit into your single theater. You are now planning the length of its run. Your share of the film’s projected box office is
R = 10 W -0.25 (W)^2, where R is in thousands of dollars and W is the number of weeks that the movie runs. The average operating cost of your theater is AC =MC = $5 thousand per week.
You realize that your typical movie makes an average operating profit of $1.5 thousand per week. How does this fact affect your decision in part a above if at all?
In: Economics
Even within a particular chain of hotels, lodging during the summer months can vary substantially depending on the type of room and the amenities offered. Suppose that we randomly select 50 billing statements from each of the computer databases of the Hotel A, the Hotel B, and the Hotel C chains, and record the nightly room rates. The means and standard deviations for 50 billing statements from each of the computer databases of each of the three hotel chains are given in the table.
| Hotel A | Hotel B | Hotel C | |
| Sample average ($) | 135 | 160 | 105 |
| Sample standard deviation | 17.2 | 22.2 | 12.1 |
(a) Find a 95% confidence interval for the difference in the
average room rates for the Hotel A and the Hotel C chains. (Round
your answers to two decimal places.)
$ to $
(b) Find a 99% confidence interval for the difference in the
average room rates for the Hotel B and the Hotel C chains. (Round
your answers to two decimal places.)
$ to $
(c) Do the intervals in parts (a) and (b) contain the value
(μ1 − μ2) = 0?
Yes, the interval in part (a) contains (μ1 − μ2) = 0.Yes, the interval in part (b) contains (μ1 − μ2) = 0. Yes, both intervals contain (μ1 − μ2) = 0.No, neither interval contains (μ1 − μ2) = 0.
Why is this of interest to the researcher?
If (μ1 − μ2) = 0 is contained in the confidence interval, it is implied that the room rate for one of the hotels was $0.If (μ1 − μ2) = 0 is contained in the confidence interval, it is implied that there is no difference in the average room rates for the two hotels. If (μ1 − μ2) = 0 is contained in the confidence interval, it is implied that there was an error in the database records.If (μ1 − μ2) = 0 is contained in the confidence interval, it is implied that there is a difference in the average room rates for the two hotels.If (μ1 − μ2) = 0 is contained in the confidence interval, it is implied that the average room rate for the two hotels was $0.
(d) Do the data indicate a difference in the average room rates
between the Hotel A and the Hotel C chains?
Yes, the data indicate a difference in the average room rates between the Hotel A and the Hotel C chains.No, the data do not indicate a difference in the average room rates between the Hotel A and the Hotel C chains.
Do the data indicate a difference in the average room rates between
the Hotel B and the Hotel C chains?
Yes, the data indicate a difference in the average room rates between the Hotel B and the Hotel C chains.No, the data do not indicate a difference in the average room rates between the Hotel B and the Hotel C chains.
In: Math
The Park Manager at Fort Fisher State Park in North Carolina believes the typical park visitor spends at least 90 minutes in the park during summer months. A sample of 18 visitors during the summer months of 2011 revealed the mean time in the park was 96 minutes with a standard deviation of 12 minutes. At the 0.01 significance level, is it reasonable to conclude that the mean time in the park is greater than 90 minutes? What is alpha?
In: Statistics and Probability
You are the manager of a theater. At present, the theater charges the same admission price of $8 to all customers, regardless of age. You propose a two-tier pricing scheme: $5 for children under the age of 12 and $10 for adults. You tell your supervisor that your proposal is likely to increase revenue. "What must be true about the price elasticity of demand if your proposal is to achieve its goal of raising revenue?
1) Explain the concepts of cross-price elastic of demand, using one of the examples in the table above. What does a positive or negative value indicate? When doing elasticity of demand what is the sign always for a normal good?
2)Explain the concepts of income elasticity using one of the items in the table above. What does a positive value indicate? What about a negative value indicate?
3) When the price of Bob’s Coffee House increased by 8 percent, the quantity demanded of Alex’s Coffee House increased by 10 percent. What would be the cross- price elastic of demand between Bob’s & Alex’s coffee? What is the relationship between these two goods (are they compliments?)
4) Suppose the current price of oil is $90 a barrel and the quantity supplied is 800 million barrels per day. If the price elasticity of supply for oil in the short run is estimated at 0.5, use the midpoint formula to calculate the percentage change in quantity supplied when the price of oil rises to $98 a barrel.
In: Economics
1. Harley's employer gave him $5,000 to cover expenses for an upcoming sales trip. He is not required to provide any receipts for his expenses, and if his actual expenses are less than $5,000, he does not have to return any money to his employer. His actual expenses for the trip were as follows:
Airfare and rental car $2,000
Meals $1,500
Hotel $1,000
Tickets to theater for a client and him $200
Total $4,700
What the income tax consequences to Harley and his employer?
| a. |
Harley: $4,700 of non-taxable reimbursed expenses, $300 of wage income, and pays half the FICA tax on the wage income Employer: Deductible expenses for airfare ($2,000), meals ($750), hotel ($1,000), wages ($500) , and pays half the FICA tax on the wage expense |
|
| b. |
Harley: $5,000 of wage income and pays half the FICA tax Employer: $5,000 of wage expense and pays half the FICA tax |
|
| c. |
Harley: $4,500 of non-taxable reimbursed expenses, $500 of wage income, and pays half the FICA tax on the wage income Employer: Deductible expenses for airfare ($2,000), meals ($1,500), hotel ($1,000), wage expense of $500 , and pays half the FICA tax on the wage expense |
|
| d. |
Harley: $3,750 of non-taxable reimbursed expenses, $1,250 of wage income, and pays half the FICA tax on the wage income Employer: Deductible expenses for airfare ($2,000), meals ($750), hotel ($1,000), entertainment ($200) wage expense of $300, and pays half the FICA tax on the wage expense |
2. Which of the following is a deductible business expense?
| a. |
Bribes paid to the mayor that are illegal under state law that is generally enforced. Violation of this law could result in up to 12 months in jail. |
|
| b. |
Wages paid to employees by a drug dealer |
|
| c. |
Wages paid to employees of an illegal gambling establishment |
|
| d. |
A speeding ticket received by the company's top salesperson while visiting customers |
3. Which of the following business expenses would not be deductible because it is not ordinary, necessary, or reasonable?
| a. |
$1,200 for employee snacks and beverages purchased from an unrelated party. |
|
| b. |
$3,000 to rent a billboard for advertising from an unrelated party. |
|
| c. |
$10,000 of fees paid to an unrelated attorney to negotiate and draft a sales contract with the company's largest customer. |
|
| d. |
$300,000 of rent paid to the sole shareholder of the company for a warehouse that is owned personally and used to house the company's inventory. The market value to rent a similar warehouse in the same area is $175,000. |
In: Accounting
In: Economics
A movie theater manager believes the average amount of money customers spend on snacks is over $15.
To test the claim, a theater employee tracks the spending of 25 randomly selected customers.
The sample mean is $17.08 with a sample standard deviation of $4.81.
a) What is the Null Hypothesis and the Alternative Hypothesis for the manager’s claim?
b) Assuming the population is normal, should we use the Normal z-test or the Student’s t-test?
In: Statistics and Probability