Summarize key data distribution concepts including probability mass functions (PMF), probability density functions (PDF), and cumulative distribution functions (CDF). Based on your organization or any organization you are most familiar with, provide an example of a PMF, an example of a PDF, and an example of a CDF, based on the type of data used in the organization. How would you summarize each of these to someone who is not familiar with each of these functions?

40% of all customers who enter a store will make a purchase. Suppose that 6 customers enter the store and that these customers make independent purchase decisions.

Round answers to four decimal places.

(1) Calculate the probability that exactly five customers make a purchase.

Probability               

(2) Calculate the probability that at least three customers make a purchase.

Probability             

(3) Calculate the probability that two or fewer customers make a purchase.

Probability             

(4) Calculate the probability that at least one customer makes a purchase.

Probability               

Bulloch County has never allowed liquor to be sold in restaurants. However, in three months, county residents are scheduled to vote on a referendum to allow liquor to be sold by the drink. Currently, polls indicate that there is a 60% chance that the referendum will be passed by the voters. Phil Jackson is a local real estate investor who is eyeing a closed restaurant building that is scheduled to be sold at a sealed-bid auction. Phil estimates that if he bids $1.25 million, there is a 25% chance he will obtain the property; if he bids $1.45 million, there is a 45% chance he will obtain the property; and if he bids $1.85 million, there is an 85% chance he will obtain the property. Phil’s intention is to sell the property after the vote is finalized and the results are made public. If he acquires the property and the referendum passes, Phil believes he could sell the restaurant for $2.2 million. However, if he acquires the property and the referendum fails, he believes he could sell the property for $1.5 million.

1. Develop and solve a decision tree to determine how much Phil Jackson should bid for the property.

a. NOTE: Due to the nature of this problem, a bid is considered a cost (not revenue). In other words, Phil is not winning an award (i.e. contract) that will pay him to complete a certain task. Phil is trying to place an offer that will result in him owning the property. Therefore, the bid is a cost.

2. Phil has limited confidence in the exit polls suggesting that there is a 60% chance that the referendum will pass. Thus, he would like to understand if he is about to make a risky decision. To further investigate this scenario, we would like to investigate how quickly the decision might change based on a changing probability of the referendum passing.

a. To answer this question, develop a Data Table in Excel that varies the probability of success from 0% to 100% using step sizes of 1%. Your table should not only contain this probability, but it should also output the decision that would be made based on the probability as well as the expected value given the probability.

3. After your table is developed, create a table that summarizes the number of instances that each bid amount decision would be made based on the Data Table.

a. In addition, record the minimum and maximum probability for each decision.

4. Finally, create an XY scatter plot for the expected value (y-axis) and probability of success (x-axis).

1. Project A
Moderate prematurity refers to babies who are born between 28 and 32 completed weeks gestational age with a birth weight range between 1500 and 2500 grams. The length of time a baby has spent in the womb, or more specifically the number of completed weeks of frequency, is called gestational age. Based on their gestational age and their weight, premature babies are placed into categories of mild, moderate and extreme prematurity. • Mild Prematurity refers to babies who are between 33 and 36 completed weeks of gestation and /or have a birth weight between 1500 and 2500 grams. • Moderate Prematurity refers to babies who are born between 28 and 32 completed weeks of gestation with a birth weight range between 100 and 1500 grams. • Extreme Prematurity refers to babies who are born before 28 completed weeks of gestation or a birth weight less than 1000 grams.
a. Generally speaking, the gestation time for human babies is approximately normally distributed, with an average of 40 weeks and a standard deviation of two weeks. i. Calculate the probability of having a birth with mild prematurity. ii. What is the probability of having a birth with extreme prematurity? iii. Find the upper and lower quartiles for the gestation times. iv. Would it be unusual to deliver a baby after only 24 weeks of gestation? v. A randomly selected baby would be an age of less than x weeks to be one of the bottom 20% in gestational age. What is the value of x? vi. Before what gestational time does 83.4% of gestational time occur? b. The birth weight of a baby is approximately normally distributed with an average of 3.4 kg and a standard deviation of 800 grams. i. Calculate the probability of having a birth with moderate prematurity. ii. What is the probability of having birth with extreme prematurity? iii. What is the probability of having a baby weighing at least 6 kg? Do you think it is highly unlikely to have a baby with this weight? explain? iv. A randomly selected baby will weigh more than x kg to be one of the top 5% in weight. What is the value of x? v. Above what weight do 87.7% of the weights occur? vi. Suppose on another planet the baby (may not be human) birth weight X follow the normal distribution. The probability that X exceeds 4 kg is 0.975 and the probability that x exceeds 5 kg is 0.95. Find µ and σ.

The sarcoplasmic reticulum Ca2 ATPase (SERCA) pumps Ca2 out of the cytoplasm and into the sarcoplasmic reticulum of muscle cells. Muscle contraction occurs in response to the rapid rise of Ca2 in the cytoplasm. Calcium ions must be removed form the cytoplasm for muscle relaxation to occur. SERCA removes the calcium ions, enabling muscle relaxation. SERCA is a monomeric protein with a nucleotide-binding domain (N), a domain that accepts a phosphoryl group (P), and an actuator domain (A). A transmembrane domain binds calcium ions.

From what you know of the mechanism of Ca2 transport, which of the following binding patterns are observed at any point? Select all that apply. Assume that only the species mentioned are bound. For example, if ADP is not mentioned, it is not bound.

Select all that apply. (Four correct answers)

2 Ca2 , ADP, and Pi bound

ADP bound

2 Ca2 and Pi bound

AMP bound

2 Ca2 bound

Pi bound

2 Ca2 , ATP bound

Prof. X has two brilliant students Y and Z in his class. He introduces the
concept of vector spaces, bases and dimension in his 5th session. As an exercise,
he gives a vector space V of dimension n and asks Y and Z to find a basis. Y
produces a set S with n elements. But Z being lazy, takes the set S, removes
a vector and adds a new vector to it creating a new set T. Prof. X looks at set
T and confirms to class that it is a basis. He then asks the class if the set S
produced by Y could be a basis without telling them what it is. While student
U says yes, student W says need not and Prof. X says that both U and W
could be correct. Justify the statement of Prof. X with suitable examples of V
over F, n, S and T.

An activated sludge process with an aeration basin volume of 0.3 MG is treating wastewater with the average daily flow of 2 MGD. The raw sewage entering the treatment plant has an average BOD5 of 400 mg/L. The primary treatment removes 25% of BOD5 and the subsequent activated sludge process is designed to remove 90% of BOD5.

Given:

Plant effluent BOD5 concentration = 30 mg/L

Biomass concentration in the aeration tank = 2,000 mg/L

Biomass concentration in the plant effluent = 20 mg/L

Biomass concentration in the recycle (RAS) = 8,000 mg/L

Flow rate of waste sludge (WAS) = 0.025 MGD

Endogenous decay rate (kd) = 0.01 day-1

a) Calculate the MCRT of the process.

b) Determine the yield coefficient, Y.

c) If µnet, nitrifiers = 0.2/day, would you expect to get nitrification in this system? Briefly describe why or why not and show any supporting calculations.

Which statements describe the structure of lymphatic capillaries?

-Lymphatic capillaries have a layer of smooth muscle in their walls.

-Collagen filaments anchor the endothelium to loose connective tissue.

-The endothelial cells are not tightly joined together.

-Lymphatic capillaries are part of a closed circuit.

Which of the cells are lymphoid cells (lymphocytes)?

-B cells

-antigens

-helper T cells

-hematopoietic stem cells

Which leukocyte can destroy microorganisms and remove cell debris?

-plasma cell

-dendritic cell

-macrophage

-T lymphocyte

Which is a function of lymph nodes?

-to filter out toxins, such as alcohol

-to store platelets

-to filter out old, damaged red blood cells

-to filter out foreign material and cell waste

What is the lymph‑related function of the appendix?

-secretes lipases that break down triglycerides

-connects the small intestine to the lymph nodes

-removes excess fluid from the small intestine

-protects the intestines from foreign antigens

Many economists favor a carbon tax as a way to discourage CO2 emissions. Suppose such a tax were to be set at $20 per ton (907kg) of carbon emissions as (CO2). Consider a 50-MW, 35% efficient power plant that uses coal with a carbon intensity of 24gC/MJ.

a. How much per year would this power plant pay in carbon tax?

b. Suppose a tree plantation sequesters (removes from the atmosphere and stores in biomass) 20,000kg of carbon dioxide per year per acre over the next 40 years the trees are growing (after which time the forest is mature and no further accumulation occurs). What area of forest would have to be planted to offset the power plant’s emissions over the next 40 years (roughly the lifetime of the power plant)?

c. What is the maximum the power plant owners would be willing to pay for this forest per acre? (do not use discounting)