You are an industrial chemist working for a company that makes methanol (CH3OH) according to the equilibrium reaction shown below. You love your job, except that your assistant does not have the best notebook keeping skills. One day you set up the reaction with the equilibrium concentrations shown below.

CO (g) + 2 H2 (g) <--> CH3OH (g) 0.24 M 1.1 M 0.15 M at 327oC

Later on your assistant mentions that he added some more CO, but he doesn't remember how much. But he also remembers that as the equilibrium was being reestablished, the hydrogen concentration changed by 0.3 M, although he doesn't remember if it went up by that much, or down by that much. How much carbon monoxide did he add, in M?

You are planning a study of attitudes to the length of jail sentences for homicide, using a scale running from –4 to +4, where 0 indicates a judgment that current sentences are about right. Previous research suggests that the population SD for the scale is 1.2. You plan to use a single sample and would like to be able to detect a true effect of 0.5 scale units, using α = .01. If you use N = 100, using the same scale to compare attitudes in two very different neighborhoods. You would like to be able to detect a difference of 0.3 scale units. Consider power and make recommendations.

This is an exercise problem in one of the textbook by Geoff Cummings, Understanding The New Statistics, this is the first problem of chapter 12. This is all the information that it has and I must come with an answer regarding power and recommendations.

Problem: Using the alternative-parameter method, determine the parameters of the following distributions based on the given assessments.

Find the parameter value β for the exponential distribution given:

P_E (T ≤ 15 \ β) = 0.50.

Find the parameters μ and s for a normal distribution given:

P_N (Y ≤ 25\ μ, s) = 0.25 and P_N (Y ≤ 125\ μ, s) = 0.75

Find the Min, Most Likely, and Max for the triangular distribution given:

P_T (Y ≤ 15\Min, Most Likely, Max) = 0.15

P_T (Y ≤ 50\Min, Most Likely, Max) = 0.50, and

P_T (Y > 95\Min, Most Likely, Max) = 0.05

Find the parameters values a₁ and a₂ for the beta distribution given:

P_B (Q ≤ 0.3\a_1, a₂) ₌ 0.05 and P_B (Q ≤ 0.5\a_1, a₂) ₌ 0.25

Basic calculations based on the Central Limit theorem: Determine the appropriate ^µ_X and σ_X given the population mean is 1020, σ is 153, and with a normal x-distribution, if Basic calculations based on the Central Limit theorem: Determine the appropriate ^µ_X and σ_X given the population mean is 1020, σ is 153, and with a normal x-distribution, if

a) n=16

b) n=50

c) n=1000

8) Determine the following probabilities given a normal x-distribution(convert to z first):

(a) µ is 8, σ is 17 with n = 64. Find P(_X>9).

(b) µ is 20, σ is 3 with an n = 36. Find P(_X<19).

(c) µ is 32, σ is 0.3 with an n = 20. Find P(31.8<_X<31.9).

The following information is given for a stock. Investors assume that the return of the stock is best explained by a two-factor model that includes the market factor and a second risk factor. Using a dividend discount model, what is the price for this stock?

Stock covariance with the market= 0.5

Market variance = 0.25

Stock covariance with a second risk factor= 0.6

variance of the second factor= 0.3

Market Premium:3%

Second factor risk premium=1%

Risk free rate =2 %

Current earnings per share= $5,

The ROE is expected to shrink (decrease) at the rate 10% for first 5 years

The ROE is expected to grow at the rate 8% forever after the first 5 years

Payout for the first 5 years: 50%

Payout after 5 years: 50%

a. Suppose that the annual interest rate is 1% and no dividend will be declared for the index constituent stocks in the coming quarter. The index is currently standing at 25,500.

i. Compute the index futures deliverable in exact 3 months.

ii. Suppose now the dividend yield of the index constituent stocks is 0.3% rather than 0%. Without doing any calculation, explain whether the index futures price is higher or lower than your answer in part (i).

b. A silver futures contract requires the seller to deliver 5,000 Troy ounces of silver. Henry sells four July silver futures contract at a price of $16 per ounce. The initial margin is $6,000 per contract and the maintenance margin is $2,500 per contract. What is the futures price per ounce at which Henry would receive a margin call?

A biotech manufacturing company can make test kits at a cost of $ 20.00. Each “kit” for which there is a glove demand the week it is manufactured can be sold for $ 100.00. However, due to the short life of its components, each “kit” that cannot be sold during that week has to be discarded at a cost of $ 5.00

The weekly demand for that product is a random variable with the following pmf

a) Calculate the expected value of the demand for “kits” during one week

b) Calculate the variance of demand for a week

c) The company could manufacture 50 “kits” per shift. If they decide to go into business, how many shifts must they work (1, 2, or 3) to maximize the expected profit?

Assume you are given two resistors with resistances R1=4.0 kΩ and R2=6.0 kΩ and two capacitors with capacitances C1=4.0 µF and C2=6.0 µF.

a) Calculate the equivalent resistances Req and the equivalent capacitance Ceq if the resistors are connected in series and the capacitors are connected in parallel.

b) Now, use the Req and Ceq that you calculate in part (a) to construct an RC circuit. If an emf of 27 V is suddenly applied across Req and Ceq, calculate the current through the Req after t = 12 µs.

c) If the resistor R1 is made of iron wire with radius R= 3 mm, calculate the length of this wire. The resistivity of iron is ρiron= 9.68x10-8 Ω.m.

d) If the capacitance C2 has square parallel-plates with the separation of 0.3 mm, calculate the plate area A.

FINANCIAL ANALYSIS

Consider the following statistics (calculated based on simple ratios with only same year data and no averaging or past year data) to answer the questions:

Total Asset = $100,000, Working Capital ratio = 1.5:1, ROE = 22%, Gross Profit Margin = 15%, Quick ratio = 0.3:1, Cost of Goods Sold = $10,000; All other expenses = $5000

A) By showing working, state what is ROA?

B) By showing working state what is the debt ratio?

C) What is the net worth of the business?

D) By showing working, what is return on sales?

Comment on the following:

i) Profitability status

ii) Liquidity Status

iii) Inventory levels

iv) Current assets excluding inventory

v) Likely cash position

The following information is given for a stock. Investors assume that the return of the stock is best explained by a two-factor model that includes the market factor and a second risk factor. Using a dividend discount model, what is the price for this stock?

Stock covariance with the market= 0.5

Market variance = 0.25

Stock covariance with a second risk factor= 0.6

Variance of the second factor= 0.3

Market Premium:3%

Second factor risk premium=1%

Risk free rate =2 %

Current earnings per share= $5,

The ROE is expected to shrink (decrease) at the rate 10% for first 5 years

The ROE is expected to grow at the rate 8% forever after the first 5 years

Payout for the first 5 years: 50%

Payout after 5 years: 50%