Two friends, Alysha and Laura, are planning for their retirement. Both are 20 years old and plan on retiring in 40 years with $1,000,000 each. Laura plans on making annual deposits beginning in one year (total of 40 deposits) while Alysha plans on waiting and then depositing twice as much as Laura deposits.

If both can earn 7.4 percent per year, how long can Alysha wait before she has to start making her deposits? (Round answer to 2 decimal places, e.g. 125. Do not round your intermediate calculations.)

An IE performed a time study on a hydraulic valve installation & test process. Each observed installation was performed by a different production worker, so the activity factor (performance rating) varied in each observation. A factor > 1.00 meant the worker was performing better than normal in their observed time (OT) (i.e, faster), while a factor < 1.00 meant the worker was performing less normal in their observed time (OT) (ie, slower). The allowance for personal delay and fatigue as was 13% for all data points. Using the data in the table, determine:

Questions  

A. What is the average standard time per valve?

B. From the time study problem above: if a worker was able to install 7 valves during an 8 hour period, what would the efficiency be?

C. From the OEE problem above, suppose an industrial engineer determined the lighting (once adequate for accurately and quickly reading print) had become too low due to the installation of new equipment that cast shadows on the ground level. In addition, the drawing formats and orientation were not standardized across the classes of ships being produced due to outsourcing efforts. By improving the lighting, standardizing the engineering drawings and re-training all workers on how to read the new drawings, the total produced parts during a similar production period was increased from 800 to 1120, while still only producing 40 defective parts. What would the new OEE value be with these improvements?

Four tourists plan on taking a bus tour around Toronto. This tour allows them to hop on and off the bus at any of the 8 stops available. The available stops are the CN tower, Harbour Front, Queen’s Quay, Dundas Square, Casa Loma, Distillery District, Bata Shoe Museum and the Royal Ontario Museum.

1. What is the probability that two attend one location and two attend another same location?
2. What is the probability that no tourists hop off at the Distillery District and Bata Shoe Museum?
3. What is the probability that at least one tourist gets off at Casa Loma?

One attempt was to investigate the effect of two treatments on the formation of tartar in dogs. In addition to the two treatment groups, there was also a control group. in the trial included 26 dogs randomized to one of the three treatment groups (follow normal distribution):

1. P2O7

2. HMP

3. Control (standard feed)

the values are given:

Group 1=(P2O7) 2= (HMP) 3=(Kontrol)

ni 9 8 9

mean 0.7467 0.4375 1.0889

s^2 0.13655 0.08448 0.17854

question: Use Bartletts test to test if the variance are equal

If possible answer in R. If not by hand is also good.

1. When σ is unknown and the sample is of size n ≥ 30, there are two methods for computing confidence intervals for μ.

Method 1: Use the Student's t distribution with d.f. = n − 1.
This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method.

Method 2: When n ≥ 30, use the sample standard deviation s as an estimate for σ, and then use the standard normal distribution.
This method is based on the fact that for large samples, s is a fairly good approximation for σ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution.

Consider a random sample of size n = 36, with sample mean x = 45.1 and sample standard deviation s = 6.0.

(a) Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

(b) Compute 90%, 95%, and 99% confidence intervals for μ using Method 2 with the standard normal distribution. Use s as an estimate for σ. Round endpoints to two digits after the decimal.

(d) Now consider a sample size of 81. Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

(e) Compute 90%, 95%, and 99% confidence intervals for μ using Method 2 with the standard normal distribution. Use s as an estimate for σ. Round endpoints to two digits after the decimal.

2. The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages.

(a) Use a calculator with mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

(b) Compute a 90% confidence interval for the population mean μ of home run percentages for all professional baseball players. Hint: If you use the Student's t distribution table, be sure to use the closest d.f. that is smaller. (Round your answers to two decimal places.)

(c) Compute a 99% confidence interval for the population mean μ of home run percentages for all professional baseball players. (Round your answers to two decimal places.)

Case study 1 part 1- Neurological disorders (20 marks total) Mary-Lou is a 75-year-old widow, who lost her husband to cancer over a year ago. Her family and friends have noticed that she has been very teary, has low self-esteem and has lost interest in the things she used to love such as going to bingo with her friends and gardening. Her family initially put this down to the loss of her husband and thought it would pass with time. However, they are now getting really concerned as they have noticed that her mood is not improving still. When asked by her daughter if she is sleeping well, she says she has been drinking wine every night to help her go to sleep. It makes her feel happy and relaxed. What started as one glass a night has now increased to two or three glasses a night, and she has also started drinking during the day. Her daughter has noticed that her mum’s face always appears flushed and that she has had quite a few colds lately. Mary-Lou is also losing her balance and experiencing mood swings. Her daughter is worried that she is relying too heavily on alcohol and fears that she is starting to get short-term memory loss from the alcohol consumption. She has been forgetting things such as where she put her keys, whether she turned on the washing machine, why she opened the fridge and forgetting the topic of conversation when talking with her daughter on the phone. Mary-Lou has also been getting disorientated and getting lost when she goes out on her daily walks. A neighbor rang her daughter one day to tell her that she found Mary-Lou wandering around aimlessly, and when questioned what she was doing Mary-Lou snapped and said she was trying to get home. Her daughter decided it was time to take Mary-Lou to the local GP to work out what was going on with her. After listening to the signs and symptoms Mary-Lou was experiencing, the GP diagnosed her with depression and prescribed 50 mg of Fluoxetine/Prozac daily. Based on the results of clinical and radiological assessments, the GP determined that she had early onset Alzheimer’s disease. He prescribed a cholinesterase inhibitor and gave them information on support groups and tips on what to do from here on in. He also prescribed 10 mg of Diazepam daily to help with the withdrawals from alcohol abuse.

Question 1 Based on the clinical picture presented above, you should have identified three diseases/conditions we have covered in BIOL122. • Name two of the diseases/conditions you identified, and • List two characteristic signs or symptoms (per disease) that you noted in Mary-Lou’s history and clinical picture. • Finally, explain the pathophysiology of both diseases/conditions you named (i.e., explain the changes that cause the disease and relate the typical signs and symptoms of the disease to the clinical picture).

Question 2 Explain the mechanism of action of two drug types Mary-Lou is prescribed with and describe how these drug actions help mitigate some of her symptoms. In you answer, make references to the pathophysiology of the relevant diseases.

Question 3 a) Identify and explain two pharmacokinetic factors that are characteristic of/specific to MaryLou’s antidepressant medication. Discuss how her age impacts the pharmacokinetics of her medication. b) Explain what specific considerations need to be made in the present scenario, when two drugs are administered simultaneously.

Question 4 Based on her clinical picture and history, explain if Mary-Lou suffers from alcohol addiction. Support your answer with relevant evidence from the case study. Define physical and psychological dependence and explain if signs and symptoms of either can be observed in Mary-Lou’s case.

Case study 1 part 2- Musculoskeletal disorders (20 marks total) Mary-Lou’s family was happy with the management plan established by the doctor as Mary-Lou was progressing quite well. She was using notepads to jot down reminders, a pillbox to keep her medication organized and a calendar to record appointments. Her family members were helping her with routine tasks such as cooking and paying bills. She was feeling much happier and did not have to rely on alcohol to go to sleep. On one particular day she was feeling so good she decided to walk to her GP appointment alone. On her way there she stumbled over a branch and fell. She felt excruciating pain in her hip. A passer-by called an ambulance and she was taken to the emergency department at the Royal Melbourne hospital. An X-ray revealed that she had broken the neck of her femur and had to have surgery to repair it. Mary-Lou wondered whether this was linked to the crepitus she had been experiencing in her joints. Her joints did feel quite stiff and painful lately. The specialist explained to Mary-Lou that the crepitus was likely due to degeneration of her cartilage and said that the fracture might have been due to weakened bones. He told her he would like her to have a bone mineral density test to measure her bone density. The DEXA scan gave a T-score of -3.0. Mary-Lou is now given bisphosphonates and told to increase her daily intake of calcium.

Question 5 Discuss the pathophysiology of the condition causing the crepitus Mary-Lou is experiencing in her joints. In your answer, list at least two more signs and symptoms associated with the disease.

Question 6 Discuss how the aetiology of Mary Lou’s joint disease differs from the other joint disease we covered in BIOL122.

Question 7 Discuss why Mary-Lou’s fracture may take longer to heal than it would for someone who was half her age. In your answer, you are expected to name and discuss three physiological factors that are needed for healing to take place and explain how each of the factors you identified is affected by ageing. Finally, name two complications of hip fracture that are prevalent in the elderly. .

Question 8 Considering Mary-Lou’s T-score, identify the condition she suffers from, briefly describe the pathogenesis of this disease, and explain why bisphosphonate administration is helpful in this condition.

1. A speaker is placed at the opening of a long horizontal tube. The speaker oscillates at a frequency of f creating a wave that moves down the tube. The wave moves through the tube at a speed of v=330 m/s.  At time t= 0s an air molecule at x=1m is at the maximum displacement of 5 nm. At the same time another molecule at x=3.7m has a displacement of 3.5nm. What is the wave function of the sound?

Shown below is the activity for one of the products of Lawrence Creations:

January 1 balance, 80 units @ $50

Purchases:

January 19: 40 units @ $51

January 22: 30 units @ $52

January 29: 40 units @ $54

Sales:

January 13: 30 units @ $80

January 23: 50 units @ $80

January 31: 45 units @ $82

Required: Lawrence Creations uses a Period Inventory System. Compute ending inventory as of January 31 and sales, cost of goods sold and gross profit for the month of January for each of the following inventory cost flow assumptions:

a. FIFO b. Weighted Average c. LIFO

2. Dataset B consists of the values {10,12,14,24,25,27,28,30,30,32,33,33,34,37,38,38,40,41,43,

44,44,46,47,49,56,58}.

(a) What is the median of Dataset B?

(b) To one decimal, what is the sample standard deviation of Dataset B? (Don’t calculate this out by hand.)

(c) Make a table of the frequency distribution (not the relative frequency distribution) of Dataset B, using the intervals 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. Be sure to appropriately label the table headings.

(d) Make a graph of the relative frequency distribution (not the frequency distribution) of Dataset B, using the intervals 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. Be sure to appropriately label the horizontal and vertical axes.

Please calculate the payback period, IRR, MIRR, NPV, and PI for the following two mutually exclusive projects. The required rate of return is 15% and the target payback is 4 years. Explain which project is preferable under each of the four capital budgeting methods mentioned above:

Table 1

Cash flows for two mutually exclusive projects