A novice marksman is shooting at a target 1000 feet away. The probability of his hitting the target is 0.3. Your answer should be rounded to the nearest thousandth.

a) What is the probability that he hits the target 3rd time on the 5th shot?

b) What is the probability that the number of shots he will have to make to hit the target is more than 6?

c) What is the probability that he will need 6 shots to hit the target the first time?

d) What is the probability that the number of shots he has to take to hit the target is 10 shots or fewer?

An individual makes decisions according to Bayes’ decision rule. For her current problem, she has constructed the following payoff table, and she now wishes to maximize the expected payoff.

The value of x currently is 50, but there is an opportunity to increase x by spending some money now.   What is the maximum amount that should be spent to increase x to 75?

Use the confusion matrixes to answer the questions below. Record your answers in a word document. Explain your responses and include screen shots where requested. A 5000 row dataset was used to build a model to predict if a person would accept a marketing offer for a personal loan (Personal Loan = Yes). It was partitioned into Training, Validation, and Test with the model results above.

If you were to decrease the cutoff to 0.3 how would that impact your FP and FN counts. Would they increase or decrease? Would your Model Cost increase or decrease?

A) An Olympic archer is able to hit the bull’s eye 80% of the time. Assume each shot is independent of the others. She will shoot 6 arrows. Let X denote the number of bull’s eyes she makes.

Find the mean of the probability distribution of X. Do not round

B) The GPA of students at a college has a mean of 2.9 and a standard deviation of 0.3. Scores are approximately normally distributed.

Suppose that the top 6% of students are eligible for the Honors Program. Find the GPA which is the cutoff score for students to qualify for this program. Round to the nearest hundredth.

The Red Hen company is launching its new food for sale in supermarkets throughout Michigan. The sales department is convinced that its spicy chicken soup will be a great success. The marketing department is considering an intensive advertising campaign. The advertising campaign will cost $2,000,000 and if successful produce $9,600,000 in added revenue. If the campaign is less successful (25% chance), the added revenue is estimated at only $3,600,000. If no advertising is used, the revenue is estimated at $7,000,000 with probability 0.7 if customers are receptive and $3,000,000 with probability 0.3 if they are not.

Question- Should Red Hen invest in an intensive advertising campaign?

For each of the following cases, determine whether the economy’s labour demand for unskilled workers will decrease or increase:

a) The cross-elasticity of factor demand between unskilled and skilled workers is –0.3, and government implements a policy that results in an increase in demand for skilled workers.

b) The cross-elasticity of factor demand between unskilled workers and capital is 1, and government implements a policy that results in an increase in the demand for capital.

c) The cross-elasticity of factor demand between unskilled and immigrant workers is –1, and government implements a policy that results in an increase in demand for immigrant workers.

A machine produces pipes used in airplanes. The average length of the pipe is 16 inches. The acceptable variance for the length is 0.3 inches. A sample of 17 pipes was taken. The average length in the sample was 15.95 inches with a variance of 0.4 inches.

A wastewater plant needs to reduce the methane content in water in a stripping tower to 0.3 mol %. The liquid stream is entering the tower with a flow rate of 200 mole/h and contains 0.8 mol % methane. The tower uses pure air for stripping and its temperature and pressure are held constant at 300 K and 1 atm, respectively. The equilibrium relation for methane in the air-water system is ? = 1.2?. a) Find the minimum vapor flow rate required to achieve this separation. B) Find the number of stages required if the vapor flow rate is taken as 1.2 ???? ′ .

A cylindrical pressure vessel is subjected to an internal pressure of 350psi. The initial
dimensions of the vessel prior to pressurization are a diameter of 12.00 inches, a length of 24.00
inches and a wall thickness of 0.06 inches. The material used in the vessel is steel with σy= 60,000 psi, (σ)̅ = 90,000(ε)̅ )0.2
, E = 30 × 10^6psi, ν = 0.3.

a. What amount of axial stress must be applied in addition to the stresses produced by the internal
pressure to result in yielding?
b. If the axial stress applied (in the addition to the stresses produced by the pressure) is 50,000 psi.
What is the new cylinder length?