Consider the yearly data of lumber production (in billions of board feet) in the United States given as follows:

A. Perform necessary analysis to construct an appropriate model for the series and plot the forecasts for the next four years and calculate 95% forecast limits.

Please use RStudio, and also send codes and packages/libraries used, for me to use and review, Thank you!

The annual per capita consumption of fresh bananas​ (in pounds) in the United States can be approximiated by the normal​ distribution, with a mean of 8.4 pounds and a standard deviation of 4 pounds. Answer the following questions about the specified normal distribution.​ (a) What is the smallest annual per capita consumption of bananas that can be in the top 10​% of​ consumptions?​ (b) What is the largest annual per capita consumption of bananas that can be in the bottom 5​% of​ consumption?

​(a) The smallest annual per captita consumption of bananas that can be in the top 10​% of consumptions is pounds. ​(Round to one decimal place as​ needed.)

​(b) The largest annual per capita consumption of bananas that can be in the bottom 5​% of consumptions is pounds. ​(Round to one decimal place as​ needed.)

In the United States, males between the ages of 40 and 49 eat on average 105.1 g of fat every day with a standard deviation of 4.5 g ("What we eat," 2012). Assume that the amount of fat a person eats is normally distributed.

(a) State the random variable.

(b) Find the probability that a man age 40-49 in the U.S. eats more than 110 g of fat every day.

(c) Find the probability that a man age 40-49 in the U.S. eats less than 93 g of fat every day.

(d) Find the probability that a man age 40-49 in the U.S. eats between 65 g and 100 g of fat every day.

(e) If you found a man age 40-49 in the U.S. who says he eats less than 65 g of fat every day, would you believe him? Why or why not?

(f) What daily fat level do 95% of all men age 40-49 in the U.S. eat less than?

Hair color in the United States is known to be 40% blond, 40% brown, and 20% black. Miranda does a study to see if the proportions match, and her survey showed 43 people with blond hair, 32 people with brown hair, and 15 with black hair. Use a chi-square test with a level of significance α=0.05.

1. Suppose the poverty line in the United States was set according the following test: a household is poor if its income is less than $55,999 per year. Is this an absolute or relative definition of poverty?

Group of answer choices

absolute

relative

neither absolute nor relative

both absolute and relative

2. The poverty rate is

Group of answer choices

the proportion of the population above the annual income defined as poor by the federal government

capable of being equal to zero using a relative income test

the proportion of the population falling below the annual income defined as poor by the federal government

the number of people that fall below the annual income defined as poor by the federal government

3. Noncash assistance accounts for

Group of answer choices

the majority of welfare programs provided by the federal government

an equal amount of welfare programs provided by the federal government, when compared to cash assistance

a minority of welfare programs provided by the federal government

zero percent of welfare programs provided by the federal government

4. Suppose for a particular group of the population the equilibrium wage is $22 and the equilibrium number of workers employed is 60,000. Which of the following could be an impact of sudden discrimination against workers from that group of the population?

Group of answer choices

a new equilibrium number of workers employed of 80,000

a new equilibrium wage of $18

a new equilibrium number of workers employed of 180,000

a new equilibrium wage of $26

Rainier Corporation, a U.S. corporation, manufactures and sells quidgets in the United States, Europe and the Middle East. Rainier conducts its operations in Europe and the Middle East through a German GmbH, which the company elects to treat as a branch, i.e. DRE, for U.S. tax purposes. Rainier also licenses the rights to manufacture quidgets to an unrelated company in China. During the current year, Rainier paid the following foreign taxes, translated into U.S. dollars at the appropriate exchange rate:

National income taxes in Germany                                                                                 $1,500,000

City of Munich income taxes                                                                                          $   200,000

Value added tax to German government                                                              $   400,000

Payroll tax to the German government (employer’s share of

     social insurance contributions)                                                                                  $   300,000

Withholding tax on royalties received from China                                     $   100,000
Saudi Arabian tax on what is actually a royalty                                                    $     75,000

Yemen income tax                                                                                                                    $     50,000

What amount of creditable foreign taxes does Rainier incur?  

A restaurant association says that households in the United States headed by people under the age of 25 spend less on food away from home than households headed by people ages 55-64. The mean amount spent per year by 32 households headed by people under the age of 25 is $2015 and the sample standard deviation is $113. The mean amount spent by 32 households headed by people ages 55-64 is $2715 and the sample standard deviation is $97. At α = 0.05, can you support the restaurant association’s claim?

According to a report of COVID-19 death rates in the United States from CDC as of April 6th 2020, New York has around 21.2 per 100,000 people for the death rate, which is the state with the highest number of COVID-19 cases.

a) Obtain a point estimate for the population proportion of Americans who have died from COVID-19 in New York state.

b) Verify that the requirements for constructing a confidence interval about p are satisfied.

c) Construct a 90% confidence interval for the population proportion of Americans who have died in New York since the COVID-19 pandemic.

d) Interpret the interval.

In reference to the year 2000 national census, the distribution of United States households according to type of living arrangement is given in the table below. An SRS of 500 households gives the observed frequencies, by household type, for the city of Aurora, Illinois.

Ethnic Origin    Census Percent    Observed frequency from sample

Married, with children                        25%                                                  95

Married, with no children                    20%                                                110

Single parent                                    5%                                                    35

Single individual                               15%                                                 65

One person                                      20%                                                 120

Other (roommate, etc.)                      15%                                                   75

Using a significance level of 0.05, test the claim that the Aurora distribution fits the distribution obtained by the census personnel.

Several geothermal power plants are in operation in the united states and more are being built since the heat source of a geothermal plant is hot geothermal water which is “free energy.” An 8-MW geothermal power plant is being considered at a location where geothermal water 160 degrees C is available. Geothermal water is to serve as the heat source for a closed Rankine power cycle with refringent 134a as the working fluid. Specify suitable temperature and pressures for the cycle, and determine the thermal efficiency of the cycle. Justify your selection.