1. Consider a stock with the following return information for 2015-2020

Year    Return

2015    25%

2016    -15%

2017    3%

2018    41%

2019    -6%

2020    12%

Find the following for your sample of returns: Average Return, Variance, and Standard Deviation.

2. Jamie’s portfolio consists of $15,000 in Microsoft stock and $45,000 in Coca Cola. Microsoft has an expected return of 19% annually with a standard deviation of 42%. Coca Cola has an expected return of 10% annually with a standard deviation of 20%. The correlation between the 2 stocks has been 0.3.

a) Calculate the expected return of Jamie’s portfolio

b) Calculate the standard deviation of Jamie’s portfolio

Consider a continuous culture of Bacillus subtilis bacteria, which are used to produce the enzyme amylase during the growth phase. The relevant parameters for growth of this bacteria are μ_MAX = 0.88 hr^-1, Y_X/S = 0.5 gdw/gr substrate, S₀ = 4.0 gr substrate/L, and the Monod constant K_S = 0.3 gr/L, while the protein yield during growth phase is Y_P/X (aka product parameter α) = 0.12 g protein/gdw. The chemostat is operated at a dilution rate that is 60% of the maximum growth rate. Using this information, what is the steady state rate of product formation in the chemostat culture, in units of grams protein/L-hour?

How do I find T score and Stanine when (Xbar = 66.73, σ = 5.77)

2. Adapted from Exercise 3.19 in the textbook. The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with mean 266 days and standard deviation 16 days.

(a) Between what range of days do about 95% of pregnancies last?

(b) What proportion of pregnancies last more than 170 days?

(c) What proportion of pregnancies last less than 245 days? 1

(d) What proportion of pregnancies last between 245 and 280 days?

(e) A pregnancy that lasts an amount of time 0.3 standard deviations less than the means lasted for how many days?

Star Corp has 5 million shares outstanding and no growth opportunities. It just paid a dividend of $6 per share and has a market value of $62.5 million.

a. What is the discount rate on Star’s stock?

b. The firm has an opportunity to invest in a new project. The project requires an additional investment of $1.2 million today and will generate additional earnings in the next 10 years. The first earnings amount of $0.3 million will begin one year from now and grow at 4% each year thereafter (until year 10). Assuming no taxes, calculate the NPV of the new project.

c. What will the stock price be if the firm undertakes the new project?

You are researching a population of brittle stars that varies in the number of legs that they produce. You survey the local population, and come up with the numbers below. Assume that the phenotypes you encounter represent the full range of possible phenotypes in this population.

1. Calculate the phenotypic variance in this trait.
2. Do the traits in this population appear to be normally distributed? Give an explanation of why this pattern might be observed.

3. Through a series of breeding experiments, you calculate that h2 for this population is 0.3. If no dominant alleles contribute to this trait, and there are no epistatic interactions involving the gene loci that control this trait, what is VE for this population?

#of legs: # of individuals:

5 ; 420

6 ; 189

7 ; 72

8 ; 5

9 ; 3

A study was conducted to determine if the students from the public universities
take longer to graduate than the students from the private universities. 100
students from both the public universities and private universities were
surveyed. Suppose that from the years of research, it was known that the
population standard deviations were 1.58 years and 1 year respectively. The
following data were collected. The public and private universities students took
an average of 4.5 and 4.1 years respectively with a standard deviation of 0.3.
Use a 0.01 level of significance to test the claim.
(i) State the null and alternative hypotheses.

(ii) Is there any evidence to support the claim at α =0.01?

MANUAL CALCULATION

Suppose you are a policy maker who wants to select a level of saving rate that would maximize consumption per worker. Given that output per worker is a square root of capital per worker, and 10% of capital depreciates every year.
(a) Construct a table with the following saving rates: 0.3, 0.4, 0.5 and 0.6. For each saving rate, fill the table with values for capital per worker, output per worker, depreciation per worker, consumption per worker and marginal product of capital. Do not just present at able but show all your work clearly, or you lose marks.
(b) Which saving rate would you chose and why.

**NO HANDWRITTEN ANSWERS PLEASE **

An automatic cookie machine at ACM, Inc. must deposit a specified amount of 25 0.3 grams (g) of dough for each cookie on a conveyor belt. It costs $0.03 to scrap a defective cookie. A sample of 50 cookies was drawn from the production process, which has been determined to be approximately normally distributed, and the results, in grams, can be found in worksheet tab Prob. 7-12 in the Excel file C07Data. a. What is the value of k in the Taguchi loss function? b. Determine how much the process varies from the target specification, based on the mean difference and standard deviation of the sample results. What is the expected loss per unit?

Q3)
A three-phase, Y-connected, 220 V, 13 kW, 60 Hz, six-pole induction motor has the following
parameter values in Ω/phase referred to the stator:
R1 = 0.3 Ω. R2' = 0.15 Ω
X1 = 0.5 Ω. X2'= 0.21 Ω Xm = 13.25 Ω
The total rotational losses are 450 W. The core loss is lumped in with the rotational losses. For a slip of 0.02,
and based on approximate equivalent circuit, determine:
(i) The rotor speed.
(ii) The stator current.
(iii) The power factor of the motor.
(iv) The input power of the motor.
(v) The developed mechanical power.
(vi) The efficiency of the motor.