Suppose K1 and K2 have the following distribution:
Scenario Probability return K1 return K2
w(1)    0.3 -10% 10%
w(2)    0.4 0% 20%
w(3)    0.3 20% -10%

(a) Find the risk of the portfolio with w1 = 30% and w2 = 70%.
(b) Find the risk of the portfolio with w1 = 50% and w2 = 50%.
(c) Which of the portfolios above (in part (a) and (b)), has higher expected returns?

A car rental agency is considering a modification in its oil change procedure. currently, it uses a type X filter, which cost $4.25 and must be changed every 9,000 miles along with oil (4 quarts.) Between each oil change , one quart of oil must be added after each 500 miles. The proposed filter (typeY) has to be replaced every 4,000 miles (along with 4 quarts of oil) but does not require any additional oil between filter changes. If the oil costs $1.14 per quart, what is the maximum acceptable price for the Type Y filter?

A. $7.97

B. $15.94

C. $17.93

D. 58.87

A Toyota Prius is a full hybrid electric automobile that costs $30,000 with 55 mpg. A Toyota Yaris is a normal car that runs on gasoline, and costs $15,000 with 35 mpg. After 100,000 miles, the Prius requires a battery replacement that costs $3,000. Suppose you drive 10 miles per day and 1 gallon of gas costs $4. How much would you have to spend on gas for each car after 10 years? Which car would cost you more money after 10 years? How much different are the gas prices between the Prius and the Yaris (10 miles per day x 10 years)?

You operate an auto store that sells tires. You are concerned about warranty returns on the tires. Company records show that the probability warranty repair for a tire in the first 90 day is .05. You are tracking the sales of three tires. What is the mean for this binomial distribution?

a. .15

b. .19

c .25

d. .35

ABC Trucking Company realized that on an annual basis the distance traveled is normally distributed with a mean of 50,000 miles and a standard deviation of 12,000 miles. How many miles will be traveled by at least 80% of the trucks? (Hint: Think about the left side of the normal curve!)

a. 39,920

b. 43,500

c. 41,000

d. 38,670

Complete the following conversions using dimensional analysis

1. 320 pennies to number of nickels

2. 320 nickels to number of American dollars

3. 750cm to feet

4. 750cm to miles

5. 316nm to yards

6. 12 meters/seconds to miles/hour

7. $9.50/hour to pennies/day

8. 3.5 millimeters/min to liters/hour

9. 35 centimeters/day to meters/second

10. 35 meters/seconds to miles/year

Please explain every step to help me better understand. Also, please, type out your responses so I can legibly read. Thank you so much.

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.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 69.1 and 73.
4. For the 18 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 69.1 and 73.
5. For part d), is the assumption that the distribution is normal necessary? YesNo

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.

1. What is the distribution of X? X ~ N
2. What is the distribution of ¯x? ¯x ~ N
3. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 65.6 and 66.7.
4. For the 43 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 65.6 and 66.7.
5. For part d), is the assumption that the distribution is normal necessary?  

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 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.

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.

(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