4. Bayes Theorem - One way of thinking about Bayes theorem is that it converts a-priori probability to a-posteriori probability meaning that the probability of an event gets changed based upon actual observation or upon experimental data. Suppose you know that there are two plants that produce helicopter doors: Plant 1 produces 1000 helicopter doors per day and Plant 2 produces 4000 helicopter doors per day. The overall percentage of defective helicopter doors is 0.01%, and of all defective helicopter doors, it is observed that 50% come from Plant 1 and 50% come from Plant 2. [8 points]

(i) The a-priori probability of defective helicopter doors produced by Plant 1 is:

a. 0.0001

b. 0.5

c. 0.002

d. 0.0001 * 0.5

(ii) Probability of helicopter doors produced by Plant 1:

a. 0.5

b. 0.002

c. 0.4

d. 0.2

(iii) Probability of a helicopter door produced by Plant 1 given that the door is defective is:

a. 0.0001

b. 0.5

c. 0.002

d. 0.2 * 0.0001

In the early 20th century, the French Canadian microbiologist Félix d’Hérelle used a virus called a bacteriophage (“phage”) to successfully treat some diseases caused by bacteria, such as dysentery and cholera. Subsequent experiments with “phage therapy” yielded mixed results; however, and enthusiasm quickly waned—especially once antibiotics became available in the 1940s. The therapy is not currently approved in the United States.

Phage therapy involves obtaining a pure culture of a disease-causing bacterium and exposing samples of the culture to different phages to see which ones kill the bacterium. The successful phage is then administered to a patient. For skin infections, the phage is applied directly to the infected area. For systemic diseases, the phage may be given orally or delivered intravenously.

Imagine you are part of a hospital medical team conveyed to treat Jerry, a 71-year-old diabetic patient, who has been suffering from a persistent infection on his foot. His doctor has tried multiple topical antibiotics, but the infection continues to worsen, so the doctor admitted him to your hospital for a new intravenous antibiotic treatment. To Jerry’s relief, the infection cleared up; however, two weeks later, the infection returned—worse than ever. Jerry’s doctor explains that the bacterium causing the infection is a multidrug resistant strain and that Jerry’s foot will need to be amputated.

Jerry’s sister, a nurse, mentions that she studied bacteriophages and asks the doctor whether phage therapy is a treatment option.

As a member of Jerry’s medical team, answer these questions:

• How would you respond to Jerry’s sister?

• Which type of phage would be used for phage therapy: a lytic or a lysogenic phage?

• What are the drawbacks of phage therapy? What are the advantages?

NeverReady batteries has engineered a newer, longer lasting AAA battery. The company claims this battery has an average life span of 19 hours with a standard deviation of 0.7 hours. Your statistics class questions this claim. As a class, you randomly select 30 batteries and find that the sample mean life span is 18.6 hours. If the process is working properly, what is the probability of getting a random sample of 30 batteries in which the sample mean lifetime is 18.6 hours or less? Is the company's claim reasonable? (Round your probability to four decimal places.)

Two types of instruments are compared to measure the amount of sulfur carbon monoxide in the atmosphere in an experiment on air pollution. The researchers want to determine if the two types of instruments provide measurements with the same variability. The following readings are recorded for the two instruments:

Suppose that the measurement populations are distributed approximately normally and test the hypothesis that ?_A = ?_B, against the alternative that ?_A ≠ ?_B. Use a significance level of 0.1

b) Is it advisable for a coffee shop owner to increase the price of his coffee if demand for coffee is price inelastic? Explain briefly using a diagram that demonstrates the impact on the firm’s Total Revenue.

c) Nicolas says that if income elasticity of demand for sugar is -0.7, sugar is an inferior good. Steve disagrees and claims that it is a necessity. Define income elasticity of demand and explain who is right and who is wrong with their statements above?

d) For Australian consumers of petrol, would the price elasticity of demand be greater for Shell petrol or petrol in general? Explain your reasoning

(a) Dose rate estimates for a mission to Mars consist of 1.9 mSv/d during each 180-d outbound and return flight, and 0.7 mSv/d while on Mars for nearly 2 y. What fraction or multiple of the annual ICRP occupational dose limits do the astronauts receive during total flight time and while exploring the planet each year? (b) How many days before the occupational dose limit is reached on the International Space Station where the dose rate is approximately 0.25 mSv/d?

Final answers are 14 and 5

(1 point) (a) Find the size of each of two samples (assume that they are of equal size) needed to estimate the difference between the proportions of boys and girls under 10 years old who are afraid of spiders. Assume the "worst case" scenario for the value of both sample proportions. We want a 99% confidence level and for the error to be smaller than 0.08.

Answer:

(b) Again find the sample size required, as in part (a), but with the knowledge that a similar student last year found that the proportion of boys afraid of spiders is 0.7 and the proportion of girls afraid of spiders was 0.69.

Answer:

The following data was collected from a TLC plate for 4 different compounds. The distance's traveled by each is shown below:

Spot A: 8.2 cm

Spot B: 0.7 cm

Spot C: 6.5 cm

Spot D: 1.3 cm

The spotting line was placed 1.5 cm above the base and the solvent traveled 10.5 cm from the bottom of the plate. Calculate the Rf value for each compound.

My answers to this were

A: 0.78 B: 0.067 C: 0.62 D: 0.12

I got this question wrong, can someone explain why?

Sec 2.1 Pitman "Probability"

A man fires 8 shots at a target. Assume that the shots are independent, and each shot hits the bull’s eye with a probability of 0.7

Given that he hits the bull’s eye at least twice, what is the chance that he hits the bull’s eye exactly 4 times?

P(hits the bull’s eye exactly 4 times | hits the bull’s eye at least twice)

The answer has P(hits the bull’s eye exactly 4 times) / P(hits the bull’s eye at least twice)

How is this determined???

A mixer operating at steady state has two inlets and one outlet.

- At inlet 1, superheated water vapor at 2 bar and 200°C flows with an average velocity of 1m/s

- At inlet 2, saturated water with a quality of x = 0.5 at 2 bar flows with an average velocity of 1m/s

- At the outlet, saturated water with a quality of x = 0.7 flows through a pipe 5 cm in diameter.

a) Calculate the mass flow rate through the outlet pipe.

b) Calculate the rate of heat loss to the surrounding from the mixer.