Two moles of an ideal gas originally at T = 400 K and V = 40 L undergo a free expansion;
?2 = 10?1
. Find (a) the entropy change of the gas, and (b) the entropy change of the universe?

The current price of a stock is $40, and two-month European call options with a strike price of $43 currently sell for $5. An investor who feels that the price of the stock will increase is trying to decide between two strategies: buying 100 shares or buying 800 call options (8 contracts). Both strategies involve an investment of $4,000.
a. Which strategy will earn more profits if the stock increases to $42?
b. How high does the stock price have to rise for the option strategy to be more profitable?

Please choose all correct answers. Please note that each incorrect answer will reduce the score by 10%.

WeVest Financial Advisors suggests an investment in two stocks (40% in Stock A and 60% in Stock B). They claim the investment will reduce risk through diversification, but they need proof. This is the historical returns for the two stocks.

a. Using a 40/60 split, what is the weighted average standard deviation of the two stocks? (Enter your answer as a percent rounded to two decimal places.)

b. Recalculate the standard deviation of a portfolio of the two stocks. (Enter your answer as a percent rounded to two decimal places.)

c. What is the reduction in standard deviation that results from the creation of a portfolio of the two stocks? (Enter your answer as a percent rounded to two decimal places.)

A company has two production plants: A and B. 40% of total production is produced in A and 60% in B. It is further known that 3% of A's production and 5% of B's production are defective. 14 articles produced by the company are chosen at random. What is the probability that:

a) Only 3 of the items are defective

b) At least 2 are defective?

c) Only 3 of the articles are good?

d) At most 7 items come out good

The Chan family composed of the parents (aged 40 and 42) and two children (Tom and Mary, aged 18 and 16 respectively), they have four goals that they would like to achieve:

1. To have the children (Tom and Mary) to receive university education in US
2. To accumulate enough for a luxury cruise trip in around 10 years
3. Save enough for retirement in 20-22 years.

And he is considering invest in

1. Small Cap Stocks
2. Blue Chips (Stocks)
3. Long dated High yield bonds
4. A 5 year investment grade bonds
5. Short term investment grade bond fund
6. Money market fund

If they would like to pick one investment for money invested for one goal, which investment you will suggest them to invest for each goal (i.e. Goal 1, 2 and 3) and why.

WeVest Financial Advisors suggests an investment in two stocks (40% in Stock A and 60% in Stock B). They claim the investment will reduce risk through diversification, but they need proof. This is the historical returns for the two stocks.

a. Using a 40/60 split, what is the weighted average standard deviation of the two stocks? (Enter your answer as a percent rounded to two decimal places.)

b. Recalculate the standard deviation of a portfolio of the two stocks. (Enter your answer as a percent rounded to two decimal places.)

c. What is the reduction in standard deviation that results from the creation of a portfolio of the two stocks? (Enter your answer as a percent rounded to two decimal places.)

In a group of 40 people, how many cases that two or more people have the same birthday? NOT probability, cases please.

1. A sample of 40 runners will be used to compare two new routines for stretching. The runners will be randomly assigned to one of the routines which they will follow for two weeks. Satisfaction with the routines will be measured using a questionnaire at the end of the two-week period. For the first routine, nine runners said that they were satisfied or very satisfied. For the second routine, six runners said that they were satisfied or very satisfied.

a) What is the test statistic?

b) What is the p-value?

An automobile dealer conducted a test to determine if the time in minutes needed to complete a minor engine tune-up depends on whether a computerized engine analyzer or an electronic analyzer is used. Because tune-up time varies among compact, intermediate, and full-sized cars, the three types of cars were used as blocks in the experiment. The data obtained follow.

Use α = 0.05 to test for any significant differences.

Find the value of the test statistic. (Round your answer to two decimal places.)

____________.

Find the p-value. (Round your answer to three decimal places.)

p-value = __________.

1)A researcher believes that there is a correlation between the number of cigarettes smoked per day and intelligence.  The following data were collected on 15 smokers.  Find Pearson's r.

Number of cigarettes (X) IQ score (Y)

7    10

49 6

41    15

38   5

37 12

19    4

35 19

40   11

1 3

10 3

18 22

21 17

15 12

7    9

38    13

n=15

Sum of X= 376          Sum of Y=161  

Sum of XY= 4,317

2) Interpret the findings from Question 2 in 1-2 sentences.

3)Give two examples, each time of two variables for which the Pearson's r might be expected to be between -.7 and -1.0.