a) The probability that a medical drug will cure a disease is 0.95 if the patient has the disease. The probability reduces to 0.10 if the patient doses not have the disease. If 70% of people in a selected community have the disease, find the probability that a person who has been cured actually had the disease.                               [6 marks]

b) A property sales agent estimates the probability of striking a deal will a client as follows:

I) Find the expected sales value.                                                                   [4 marks]

ii) Find the standard deviation of the sales

c) The following table shows, for a group of 12 production workers, the number of months of working experience on a particular process each of them had, and the number of defective items that they produced during a given week.

You are required to:

I) calculate the coefficient of linear correlation for the data, and comment on the result.                                                                                                          [8 marks]

ii) Determine the coefficient of determination for the data, and explain its implication.

                                                                                                                    [4 marks]

iii) Determine the equation of the least squares regression line, and comments on the values of the coefficient and the constant.                                          

1. The mean cholesterol level of 40 to 60 year-old women surveyed in a particular country was found to be 5 mmol/l with a standard deviation is 1 mmol/l. The random variable is

2. Which of the following statements is correct regarding the standard normal distribution?

3. A survey of Canadians showed the mean number of hours spent volunteering at any activity was 11 hours per year with a standard deviation of 1.5 hours. If the number of hours spent volunteering is normally distributed, what is the probability that a randomly selected person will have spent more than 15 hours volunteering over a one-year period?

4.For a uniform continuous probability distribution, the probability of observing any single observation of the random variable is equal to 1/(b-a).

5.To compute the median of a continuous uniform probability distribution we sum the minimum and maximum observations and divide the sum by 2.

6.A normal distribution refers to any symmetric probability distribution, whether discrete or continuous.

7. The total area under the normal curve

A retail store has implemented procedures aimed at reducing the number of bad checks cashed by its cashiers. The store's goal is to cash no more than eight bad checks per week. The average number of bad checks cashed is 18 per week. Let x denote the number of bad checks cashed per week. Assuming that x has a Poisson distribution:

A) Find the probability that the store's cashiers will not cash any bad checks in a particular week. (Round your answer to 4 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

(b) Find the probability that the store will meet its goal during a particular week. (Round your answer to 4 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

(c) Find the probability that the store will not meet its goal during a particular week. (Round your answer to 4 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

(d) Find the probability that the store's cashiers will cash no more than 10 bad checks per two-week period. (Round your answer to 4 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

(e) Find the probability that the store's cashiers will cash no more than five bad checks per three-week period. (Round your answer to 4 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

Applications of the Normal Distribution

Read each question carefully and show your work (ie, what you put into the calculator)!!

1. Cherry trees in a certain orchard have heights that are normally distributed with a mean of 110 inches and a standard deviation of 13 inches. What is the probability that a randomly selected tree is:

a) More than 115 inches tall?   

       (round to 4 decimals)

b) Less than 95 inches tall?    

       (round to 4 decimals)

c) Between 95 and 105 inches tall?   

       (round to 4 decimals)

2. A survey among freshmen at a certain university revealed that the number of hours spent

     studying the week before final exams was normally distributed with a mean of 25 hours and a

     standard deviation of 7 hours.

a) Calculate the 70^th percentile of the number of hours spent studying.

      (Round to the nearest whole number)

b) Find the cutoffs for the middle 70% of the number of hours spent studying.

      (Round to the nearest whole number)

3.   The Real Estate Group NY reports that the mean monthly rent for a one-bedroom apartment

       (without a doorman) in Manhattan is $2630 with a standard deviation of $400.

       A real estate firm samples 100 apartments.

a) What is the probability that the mean rent is greater than $2700?

       (round to 4 decimals)

b) What is the probability that the mean rent is between $2500 and $2600?  

       (round to 4 decimals)

1. Assume that a loss history is normally distributed with a mean of $5,000 and a standard deviation of $1,500.

a. In what range, with 95 % certainty, can we expect the losses to fall this coming year? (2 points)

b. If the risk manager is willing to tolerate 1.5% chance that costs will be greater than the maximum probable loss, what is the maximum probable loss level? (1 point)

c. What’s the probability that the next loss will be greater than $5,750? Please present your final answer in percentage format, for example, 5.58%. (1.5 points)

2. Assume the probability of having a defective product is 10% and the number of loss follows a binomial distribution

a. What’s expected number of defective products for a batch of 10,000? What is the standard deviation that associates with the number of defective products? (1 point)

b. What is the probability there will be less than 1,066 defective products next year? Use the normal approximation. (1 point)

c. In what range, with 90 % certainty, can we expect the losses to fall this coming year? (2 points)

3. Assume the number of traffic accidents that occur on a particular stretch of road during a year follows a Poisson distribution with a mean of 36. For a risk manager with a risk tolerance level of 6.30%, what would be the estimated maximum probable number of traffic accidents? (1.5 point)

2. A 1.00L piston with 1.00mole of an ideal gas at 298.0K and 1.00bar is isothermally and reversibly compressed to a final volume of 0.100L, then irreversibly expanded in 1 step to its original volume with an applied pressure of 1.00bar.

a. (6 pts) Calculate the change in heat for the system (q sys) for the compression and expansion steps.

b. (6 pts) Calculate the change in entropy for the compression and expansion steps.

Show step by step and i will rate!

Thanks!

c. (6 pts) Calculate the net change in entropy for the compression and expansion steps together.

d. (6 pts) Is there a net change in entropy for the system? If so, why; if not, why not?

e. (6 pts) Is there a net change in the entropy for the surrounding? If so, why; if not, why not?

The piston diameter of a certain hand pump is 0.7 inch. The manager determines that the diameters are normally distributed, with a mean of 0.7 inch and a standard deviation of 0.005 inch. After recalibrating the production machine, the manager randomly selects 21 pistons and determines that the standard deviation is 0.0044 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the a=0.10 level of significance?
What are the correct hypothesis is H0:_,_,__
The alternative hypothesis is H1: _,_,__
Calculate the value of the test statistic.

X2/0= _ (Round two decimal)
Use technology to determine the P-value of the test statistic.
The P-value is_. (Round three decimal places)
What is the correct conclusion at the a=0.10 level of significance?
Since the P-value is ___ than the level of significance, ___ the null hypothesis. There ___ sufficient evidence to conclude that the standard deviation has decreased at the 0.10 level of significance.

The piston diameter of a certain hand pump is 0.7 inch. The manager determines that the diameters are normally distributed, with a mean of 0.7 inch and a standard deviation of 0.005 inch. After recalibrating the production machine, the manager randomly selects 21 pistons and determines that the standard deviation is 0.0044 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the a=0.10 level of significance?
What are the correct hypothesis is H0:_,_,__
The alternative hypothesis is H1: _,_,__
Calculate the value of the test statistic.

X2/0= _ (Round two decimal)
Use technology to determine the P-value of the test statistic.
The P-value is_. (Round three decimal places)
What is the correct conclusion at the a=0.10 level of significance?
Since the P-value is ___ than the level of significance, ___ the null hypothesis. There ___ sufficient evidence to conclude that the standard deviation has decreased at the 0.10 level of significance.

Consider a container with a frictionless piston that contains a given amount of an ideal gas. Assume the initial volume of the gas is 7 L, the initial temperature of the gas is 22.1 °C, and the system is in equilibrium with an external pressure of 1.1 bar. In step 1, the gas is cooled reversibly to a final temperature -29.9 °C. The external pressure remains constant at all times. In step 2 the gas is heated at constant volume to a final temperature 4.1 °C.

A) What is the final pressure of the gas?

B) What is the final volume?

C) Calculate w for the overall process (steps 1 + 2)

A monatomic ideal gas is contanined in a cylinder with a moveable piston. Initially the volume of the cylinder is 0.25m^3. The gas is compressed under a constant pressure of 3 Pa until the volume has been halved. Then the volume is held constant while the pressure is doubled. Finally, the gas is allowed to expand isothermally back to its original condition.

a)Sketch a P-V diagram for this process. Label the corners 1, 2, 3 with 1 being the beginning point.

b) If the temperature was 27 degrees at the beginning, what was the temperature at the end of the isobaric process?

c) how many moles of gas are there? How many particles of gas are there?

d) what is the total thermal energy of the system at the beginning of the process?

e) Find the work, heat and change in thermal energy for each step of the process. Place your final answers in a chart.

I got part b by using Tfinal=Tinitial*(Vfinal/Vinital)= 150K but am not getting the correct answers for the rest part c I know I use n=pV/RT but for some reason not coming up with the correct answer. Please Help???