The price of natural gas varies from country to country. Suppose the country price is normally distributed with a mean of $5 per thousand cubic feet and standard deviation of $0.8.

(a) What is the first quartile of the price of natural gas? What is the 95th percentile of the price of natural gas? Show your work.

(b) We are analyzing a group of seven countries. What is the probability that the price of natural gas would exceed $5 in more than five of those countries? Show your work.

(c) Take two countries and assume that their prices of natural gas are independent. What is the probability that the price of gas is lower than $4 in at least one of them?

You and a team of scientists are interested in understanding whether your weight gain drug was useful to help underweight population to gain weight. For your sample of 25 people, their weight was measured before, and then post the drug administration. The difference in their weight, was measured and calculated by POST – PRE. The sample had an average difference of + 0.8 lbs, with a standard deviation of 1.5 lbs. Does your sample suggest that your weight gain drug was useful in helping underweight population gain weight? Test your hypothesis at 5% significance. a. Hypothesis and identify/calculate the critical value. (5pts) Ho: Ha: Critical Value: b. Calculate the statistics (10 pts) c. Conclusion (5pts)

In the two-period model of consumption, suppose that the first period income is $5,000 and the second period income is $5,500 for both Jill and Jack. The interest rate is 10 percent. Jack’s lifetime utility function is ?1 + ?2 while Jill’s lifetime utility function is ?1 + 0.8?2.

1)Draw a graph that represents the common budget constraint that Jill and Jack face.

2)Draw indifference curves of Jill and Jack in separate graphs and compare the slopes of the indifference curves with the slope of the budget constraint curve.

3)Determine the optimal consumption in period 1 and 2, for both Jill and Jack.

4)If there is a borrowing constraint, whose consumption is affected by that?

A project under consideration has an internal rate of return of 13% and a beta of 0.8. The risk-free rate is 3%, and the expected rate of return on the market portfolio is 13%.

a. What is the required rate of return on the project? (Do not round intermediate calculations. Enter your answer as a whole percent.)

b. Should the project be accepted?

c. What is the required rate of return on the project if its beta is 1.80? (Do not round intermediate calculations. Enter your answer as a whole percent.)

d. If project's beta is 1.80, should the project be accepted?

A ) Required rate of return__________%

B) Accept the Project = Yes or No

C) Required rate of return __________%

D) Accept the project = Yes or No

Real GDP, consumption, and the marginal propensity to consume (MPC) for five hypothetical countries are shown in the table below.

a. Enter the current level of saving in the appropriate column in the table.

b. Now suppose that GDP increases by $20 billion in each of the five countries. What would be the new level level of saving in each country? Show your answers in the table below.

Payroll Entries Widmer Company had gross wages of $314,000 during the week ended June 17. The amount of wages subject to social security tax was $282,600, while the amount of wages subject to federal and state unemployment taxes was $39,000. Tax rates are as follows: Social security 6.0% Medicare 1.5% State unemployment 5.3% Federal unemployment 0.8% The total amount withheld from employee wages for federal taxes was $62,800. If an amount box does not require an entry, leave it blank. a. Journalize the entry to record the payroll for the week of June 17. b. Journalize the entry to record the payroll tax expense incurred for the week of June 17.

The minimum and maximum values of the coefficient of determination r2 are, respectively,
A. 0 and 1
B. −1 and 1
C. −1 and 0
D. 0 and +∞

The following data represent a random sample of earwig density (x) and the proportion of males that have forceps (y).

Which of the following is the correlation coefficient?
A. 0.33
B. 0.17
C. 0.02
D. 0.8

Which of the following is the equation of the regression line?
A. y^=0.0072x+0.1452
B. y^=0.0072+0.1452x
C. y^=0.3319+0.1101x
D. y^=0.1101x+0.3319

Two types of flares are tested for their burning times (in min) and sample results are given below.

Part I : Test the claim that Brand X has a mean less than Brand Y. Use 0.05 significance level.

Claim:

Null Hypothesis:

Alternative Hypothesis:

Calculator Screen Name in Ti 183:

test statistics:

Pvalue/alpha conversion

decision:

Conclusion:

Part II: Construct a 95% confidence interval for U1-U2. Interpret the interval.

Confidence interval name on TI 83

Interval

Interpret.

The mean height of an adult giraffe is 18 feet. Suppose that the distribution is normally distributed with standard deviation 0.8 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. What is the median giraffe height?  ft.

c. What is the Z-score for a giraffe that is 20 foot tall?

d. What is the probability that a randomly selected giraffe will be shorter than 17.9 feet tall?

e. What is the probability that a randomly selected giraffe will be between 17.7 and 18.3 feet tall?

f. The 80th percentile for the height of giraffes is  ft.

The expected return of market portfolio is 10%. The standard deviation of market portfolio is 20%. Risk free interest rate is 2%. There is an investor with mean-variance utility function  Answer the following questions.

1) Calculate the optimal weight to be invested in the market portfolio for the investor with A=5 . Calculate the expected return and standard deviation of the optimal complete portfolio for the investor.

2) According to the CAPM, calculate the expected returns of two stocks (stock 1 and stock 2) with betas equal to 0.8 and 1.5 respectively.

3) Calculate the beta and expected return of the portfolio that invests 20%, 60%, and 20% on stock 1, stock 2, and the risk-free asset, respectively.