Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The actual weight of coal loaded into each car are normally distributed with a mean of 75 tons and a standard deviation of 0.8 tons.  Let  be the average coal weight of a random sample of 20 cars.

1. Calculate the mean and the standard deviation of , and describe the shape of its sampling distribution.
2. What is the probability that the mean coal weight of the random sample of 20 cars is less than 74.5 tons?

Net U.S. energy imports have decreased every year since 2016. Last year’s change in net energy trade
(crude oil, natural gas, coal, and petroleum products) in the U.S.—from 3.6 quads of net imports in 2018 to
0.8 quads of net exports in 2019—was the largest change in U.S. energy trade since 1980. How would the
low oil price affect the U.S. crude oil trade (import and export) in 2020? Apply the D-S model.

A large fish strikes bait cast by a fisherman with a rod and reel. The fish creates tension in the line of 63.7 N. How many revolutions of the reel occur in 0.8 s if the reel has a moment of inertia of 4.9 × 10-3 kg·m2 and the radial distance of the line from the reel’s axis is 3.4 cm? Assume the reel has negligible friction. (The units for your answer should be rev) I got 0.0001146 rev but it is incorrect, what did I do wrong?

Consider the reaction:

2 NO₂ (g) ⇌ N₂O₄ (g)

The ΔGf° for NO₂ (g) = 52 kJ/mol and for N₂O₄ (g) = 98 kJ/mol at 298 K.

Calculate the ΔG at the following values.

0.8 M NO₂ (g) & 3.0 M N₂O₄ (g)

4.0 M NO₂ (g) & 0.9 M N₂O₄ (g)

2.2 M NO₂ (g) & 2.4 M N₂O₄ (g)

2.4 M NO₂ (g) & 2.2 M N₂O₄ (g)

West Coast Containers manufactures a high quality container in which to ship electronic equipment. Actual production was 18,000 containers using 9,500 machine-hours. Actual variable costs were $20 per machine-hour. The current year operating budget is based on production of 20,000 containers with 0.8 machine-hour allowed per container. Variable manufacturing overhead is anticipated to be $220,000. Calculate the variable overhead rate and efficiency variances. Calculations s/b 2 decimal places.

In a sample of 50 participants, you are interested in learning about the participants' health and hygiene habits. Construct confidence interval estimates regarding student health and hygiene behavior

1a. Of the 50 participants, 33 reported seeking healthcare services at least once a year. Construct a 99% confidence interval for this, and interpret

1b. The 50 participants reported a mean of 2.5 visits to seek healthcare services per year, with a standard deviation of 0.8 times. Construct a 95% confidence interval for number of visits and interpret:

1. From the perspective of someone using aggregate-demand and aggregate supply analysis, what is the impact of a tax cut when the economy is operating above full employment. Is this a wise policy? Why or why not?

2. From your readings, what is meant by each of the following?

a) MPC

b) MPS

3. Explain briefly how spending can multiply, and then calculate the spending multiplier when the MPC is
a. 0.75   
b. 0.8       
c. 0.6    

pleas answer them by typing