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# MBA604 Statistics Assignment 1 Part 1 1) (5 pts) An electronics company is about to launch a new product. If the serial number for each piece

An electronics company is about to launch a new product. If the serial number for each piece produced has the following format: LLNNN where L stands for any letter in the English alphabet and N is a number from 0 to 9, please answer the following:
a)What is the name of the counting rule used to find all the possible outcomes?
b)How many different items can be uniquely numbered?
2)
(5 pts)
A company needs to select an expert group of consultants to provide advice for a given project. How many possible selections consisting of 2 project managers, 2
legal advisors, 4 computer scientists and 3 systemsengineers can be selected if the company can pick from 4 project managers, 7 legal advisors, 5 computer scientists and 6 systems engineers? Think carefully about the counting rules involved before attempting to do any calculations.
3)
(5 pts)
Consider that you are a line manager in your current Corporation. There is a 0.50 probability that you will be promoted this year. There is a 0.65 probability that you will get a promotion or a raise. The probability of getting a promotion and a raise is 0.35. (Use letter P to denote promotion and letter R to denote raise.)
a. If you get a promotion, what is the probabilitythat you will also get a raise?
b. What is the probability that you will get a raise?
c. Are getting a raise and being promoted independent events? Explain using
probabilities.
d. Are these two events mutually exclusive? Explain using probabilities.
Please show all the steps in your calculations
Part 2
Two of the cylinders in an eight-cylinder car are defective and need to be replaced. If two
cylinders are selected at random, what is the probability that
a. both defective cylinders are selected?
b. no defective cylinder is selected?
c. at least one defective cylinder is selected?
You are requested to solve the problem using two different approaches:
1.(9 pts) Solve the problem using your knowledge from the theory of probability (chapter 4 in your e-text). If you wish to use letters in order to label the events: please let "D
1
" denote the event of the first cylinder selected, to be defective and let "D
2
" denote the event of the second cylinder selected, to be defective. If you find it helpful
you can construct a tree diagram for this problem.
2.(9 pts) Solve the problem using your knowledge on probability distributions (chp 5 &
6). It is important to justify your choice of probability distributionto use. You will need to decide whether your random variable is continuous or discrete and also need to identify whether the sampling carried out is with or without replacement. These steps will help you to identify the appropriate probability distribution to use.
3.(2 pts) Finally compare the two solutions. Elaborate on thecomputational complexity
of each one of them and the execution time when solving the problem by hand (allowing the use of a basic scientific calculator but not statistical software).

MBA604 Statistics Assignment 1 Part 1 1) (5 pts) An electronics company is about to launch a new product. If the serial number for each piece produced has the following format: LLNNN where L stands for any letter in the English alphabet and N is a number from 0 to 9, please answer the following: a) What is the name of the counting rule used to find all the possible outcomes? b) How many different items can be uniquely numbered? 2) (5 pts) A company needs to select an expert group of consultants to provide advice for a given project. How many possible selections consisting of 2 project managers, 2 legal advisors, 4 computer scientists and 3 systems engineers can be selected if the company can pick from 4 project managers, 7 legal advisors, 5 computer scientists and 6 systems engineers? Think carefully about the counting rules involved before attempting to do any calculations. 3) (5 pts) Consider that you are a line manager in your current Corporation. There is a 0.50 probability that you will be promoted this year. There is a 0.65 probability that you will get a promotion or a raise. The probability of getting a promotion and a raise is 0.35. (Use letter P to denote promotion and letter R to denote raise.) a. If you get a promotion, what is the probability that you will also get a raise? b. What is the probability that you will get a raise? Please show all the steps in your calculations Part 2 Two of the cylinders in an eight-cylinder car are defective and need to be replaced. If two cylinders are selected at random, what is the probability that a. both defective cylinders are selected? b. no defective cylinder is selected? c. at least one defective cylinder is selected? You are requested to solve the problem using two different approaches: 1. (9 pts) Solve the problem using your knowledge from the theory of probability (chapter 4 in your e-text). If you wish to use letters in order to label the events: Let "D 1 " denote the event of the first cylinder selected, to be defective. Let "D 2 " denote the event of the second cylinder selected to be defective, when the result (defective/non-defective) of drawing the first cylinder is unknown. Therefore, P(D 2 ) is the marginal/prior probability of the 2 nd cylinder selected and being defective, without knowing the selection result of the first cylinder. To reiterate, P(D 2 ) is a marginal/prior probability, not a conditional one. If you find it helpful you can construct a tree diagram for this problem. 2. (9 pts) Solve the problem using your knowledge on probability distributions (chp 5 & 6). It is important to justify your choice of probability distribution to use. You will need to decide whether your random variable is continuous or discrete and also need to identify whether the sampling carried out is with or without replacement. These steps will help you to identify the appropriate probability distribution to use. 3. (2 pts) Finally compare the two solutions. Elaborate on the computational complexity of each one of them and the execution time when solving the problem by hand (allowing the use of a basic scientific calculator but not statistical software). It is emphasised once more that in the first case you need to solve the problem without using any known probability distribution formulas. You only need to use your knowledge from chapter 4. Show entire document 11. Include a reference and bibliographical list. Make sure you use a formal referencing scheme (e.g. Harvard, Vancouver). 12. If necessary include appendices to provide additional material relevant to the document. Minimum 1500 words, Maximum 2500 words (If you are exceeding the word limit, please move some material to the appendices) MBA604 Statistics Assignment 2 (35 pts) Problem 1 (12 pts, 2 pts per question) Consider a population of five items identical in appearance but weighing 9, 13, 15, 17, and 19 grams. 1. Determine the mean and the variance of the population . 2. How many possible samples can we have if we sample without replacement from the above population with a sample size of 2. Please justify your choice of counting rule to determine the number of possible samples. 3. Write down all the possible samples, either in a linear format (i.e. a simple list) or using a tree diagram. 4. Using the ten sample-mean values, estimate the mean of the population and the variance of x . 5. Compute the standard error of the mean. 6. What is the relevant theorem that describes the behaviour of the sample mean when repeated samples are taken? Briefly describe the theorem in your own words. Problem 2 Part A (7 pts) The bottling station in plant A of a fizzy drinks company fills cans with a nominal value of 330 ml. Five days before the annual maintenance of machinery, a sample of 16 cans is taken and the volume of liquid in each one measured. At the 5% level of significance test whether the bottling process is carried out accurately or whether the filling machinery needs calibration. Use both the critical and the p-value approaches. (You will find the data in table 1. Use only the first column of the table corresponding to plant A.) Part B (8 pts) The company owns another bottling station located in a different plant (plant B). The plant manager claims that the variance of the can volumes (in ml 2 ) of the 2 nd bottling process (plant B) is the same as that of the 1 st plant. A sample of 10 cans is taken from the bottling station in plant B and the sample standard deviation is found to be 4.001 ml. Using the value of the sample variance of plant A that you have already calculated, test the claim of the plant manager at the 5% level of significance, using the critical value approach. You do not need to use the data from table 1 that corresponds to plant B.  Show entire document
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Dear pkawesha, PFA for... View the full answer Part 1
1) An electronics company is about to launch a new product. If the serial number
for each piece produced has the following format: LLNNN where L stands for any
letter in the English alphabet...

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