The average number of miles (in thousands) that a car's tire will function before needing replacement is 66 and the standard deviation is 14. Suppose that 18 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution.
In: Statistics and Probability
The average number of miles (in thousands) that a car's tire will function before needing replacement is 66 and the standard deviation is 11. Suppose that 43 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution.
In: Statistics and Probability
A tire company has developed a new tread design and claim that the newly designed tire has a mean life of 60,000 miles or more.
To examine the claim, a random sample of 16 prototype tires is tested. The mean tire life for this sample is 60,758 miles.
Assume that the tire life is normally distributed with unknown mean µ and standard deviation σ=1500 miles.
(a) Please construct a 90% confidence interval for the mean life of the new designed tire.
Does your confidence interval support the company’s claim?
(b) How would you set up a hypothesis to test the claim?
Please use α=0.05. Is your conclusion consistent with part (a)?
In: Statistics and Probability
In C# The Saffir-Simpson Hurricane Scale classifies hurricanes into five categories numbered 1 through 5. Write an application named Hurricane that outputs a hurricane’s category based on the user’s input of the wind speed. Category 5 hurricanes have sustained winds of at least 157 miles per hour. The minimum sustained wind speeds for categories 4 through 1 are 130, 111, 96, and 74 miles per hour, respectively. Any storm with winds of less than 74 miles per hour is not a hurricane. If a storm falls into one of the hurricane categories, output This is a category # hurricane, with # replaced by the category number. If a storm is not a hurricane, output This is not a hurricane.
In: Computer Science
The following table shows the rate R of vehicular involvement in traffic accidents (per 100,000,000 vehicle-miles) as a function of vehicular speed s, in miles per hour, for commercial vehicles driving at night on urban streets.
| Speed s | Accident rate R |
|---|---|
| 20 | 1500 |
| 25 | 650 |
| 30 | 200 |
| 35 | 400 |
| 40 | 650 |
| 45 | 1300 |
(a) Use regression to find a quadratic model for the data.
(Round the regression parameters to two decimal places.)
R =
(b) Calculate
R(65).
(Round your answer to two decimal places.)
R(65) =
Explain what your answer means in practical terms.
Commercial vehicles driving at night on urban streets at miles per hour have traffic accidents at a rate of per 100,000,000 vehicle miles.
(c) At what speed is vehicular involvement in traffic accidents
(for commercial vehicles driving at night on urban streets) at a
minimum? (Round your answer to the nearest whole number.)
mph
In: Advanced Math
Suppose that you are considering the purchase of a hybrid vehicle. Let's assume the following facts. The hybrid will initially cost an additional $4,500 above the cost of a traditional vehicle. The hybrid will get 40 miles per gallon of gas, and the traditional car will get 30 miles per gallon. Also, assume that the cost of gas is $3.60 per gallon.
Instructions
Using the facts above, answer the following questions.
a. What is the variable gasoline cost of going one mile in the hybrid car? What is the variable cost of going one mile in the traditional car?
b. Using the information in part (a), if “miles” is your unit of measure, what is the “contribution margin” of the hybrid vehicle relative to the traditional vehicle? That is, express the variable cost savings on a per-mile basis.
c. How many miles would you have to drive in order to break even on your investment in the hybrid car?
d. What other factors might you want to consider?
e. Show all necessary computation to receive credit.
In: Operations Management
| 4. An airline wants to know the impact of method of redeeming frequent-flyer miles and the age group of customers on how the number of miles they redeemed. To do so, they perform a two-way analysis of variance on the data for miles redeemed shown on cells L35 to O43 on the answers sheet. | |||||||||||
| a. Identify the null and alternative hypotheses for each of the two main effects and the interaction. | |||||||||||
| b. Use two-way analysis of variance to test each of these three sets of hypotheses at the 0.05 significance level. | |||||||||||
| Methods of redeeming miles | Under 25 | 25 to 40 | 41 to 60 | Over 60 | sums | mean |
| Cash | 300,000 | 60,000 | 40,000 | 0 | ||
| 0 | 0 | 25,000 | 5,000 | |||
| 25,000 | 0 | 25,000 | 25,000 | |||
| Discount Vacations | 40,000 | 40,000 | 25,000 | 45,000 | ||
| 25,000 | 25,000 | 50,000 | 25,000 | |||
| 0 | 5,000 | 0 | 0 | |||
| Discount Internet Shopping Spree | 25,000 | 30,000 | 25,000 | 30,000 | ||
| 25,000 | 25,000 | 50,000 | 25,000 | |||
| 75,000 | 50,000 | 0 | 25,000 | |||
| sums | ||||||
| mean |
In: Statistics and Probability
1. The completion times for the government exam used for entrance into Officer Candidate School is uniformly distributed between 85 minutes and 145 minutes.
A. What is the probability someone finishes the exam between 95 and 120 minutes?
B. What is the probability it takes a candidate at least 110 minutes to finish the exam?
Make sure you round to 4 decimal places where appropriate.
2. The average daily commuting distance for a San Diegan is 31 miles with a standard deviation of 5.8 miles. If commuting distances are normally distributed:
A. What is the probability that a person commutes at most 35 miles?
B. What is the probability that a person commute is between 25 and 38 miles?
C. What would someone have to commute to be in the top 6% of longest commutes (Where does the Top 6% start)?
Make sure you round to 4 decimal places where appropriate.
When you answer the question put the 5 answers in this order and label like this:
1A.
1B.
2A.
2B.
2C.
In: Statistics and Probability
An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 256 brakes using Compound 1 yields an average brake life of 49,386 miles. A sample of 298 brakes using Compound 2 yields an average brake life of 47,480 miles. Assume that the population standard deviation for Compound 1 is 1649 miles, while the population standard deviation for Compound 2 is 3911 miles. Determine the 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.
Step 1 of 3 : Find the point estimate for the true difference between the population means.
Step 2 of 3: Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to sox decimal places.
Step 3 of 3: Construct the 80% confidence interval. Round your answers to the nearest whole number.
In: Statistics and Probability
9. As part of a study of corporate employees, the director of human resources for PNC Inc. wants to compare the distance traveled to work by employees at its office in downtown Cincinnati with the distance for those in downtown Pittsburgh. A sample of 35 Cincinnati employees showed they travel a mean of 370 miles per month. A sample of 40 Pittsburgh employees showed they travel a mean of 380 miles per month. The population standard deviations for the Cincinnati and Pittsburgh employees are 30 and 26 miles, respectively. By following the six-step procedure for hypothesis testing found below, answer the following: At the 0.05 significance level, is there a difference in the mean number of miles traveled per month between Cincinnati and Pittsburgh employees?
Step 1: State the Null Hypothesis (H_0) and the Alternate Hypothesis (H_1)
Step 2: Determine the level of significance. (Note: It’s given in this problem!)
Step 3: Select the Test Statistic
Step 4: Formulate the Decision Rule
Step 5: Make a Decision
Step 6: Interpret the Result
In: Math