Assignment 2 is designed to:
? demonstrate mastery of the subject material covered in the text, the lectures and the
tutorials for the topics Probability, Probability Distributions, Sampling and Sampling
? detect difficulties with any concepts so the lecturer can provide feedback;
? assess learning objectives 1, 3, 5, 6 and 7.
? build a base for study in the later topics.
Question 1 (24 marks)
Marks will be awarded for:
? the correct answers and appropriate detailed working, including the relevant
? appropriate well labelled diagrams;
? a sentence which answers the questions asked.
a. If ( ) 0.06 P C D ? ? , P(C) = 0.4 and P(D) = 0.2,
i) find ) | ( D C P .
ii) find ) ( D C P ? .
b. In a drawer there are 30 ribbons, 16 are blue and the rest are red. Two ribbons are
selected at random from the drawer, without replacement.
i) Draw a probability tree diagram to represent this problem. Label the end of
each branch with the simple events and include the probabilities along each
branch of the tree.
ii) If two ribbons are drawn at random what is the probability of selecting a pair
of matching ribbons (two ribbons the same colour)?
c. Given that Z is the standard normal random variable,
i) find ) 36 . 1 ( ? Z P (2 marks)
ii) find P( -1.2< Z< 2) (3 marks) An appropriate, well labelled diagram must be included for each part. d. The life time of the Tuff brand of tyres is approximately normally distributed, with a mean of 63,000 km and a standard deviation of 3,000 km. The tyres carry a warranty of 55,000 km. i) What proportion of tyres will fail before the warranty expires? An appropriate, well labelled diagram must be included (4 marks) ii) The Tuff company claims that at least 10% of the tyres last longer than 68,000 km. Provide evidence to support or disprove this statement. An appropriate, well labelled diagram must be included. (4 marks) Question 2 (14 marks) Marking Criteria Marks will be awarded for: ? the correct answers and appropriate detailed working, including the relevant formula; ? a sentence which answers the questions asked. a. On average 12 people every half hour check in at Counter A at the Qantas domestic terminal at Terminal 2 at Sydney airport. The people arrive at the counter randomly and independently. i) Identify the type of probability distribution represented by this problem and write down the value(s) of the parameter(s). (2 marks) ii) Calculate the probability of more than 13 people checking in at Counter A in the next half hour. (4 marks) iii) Calculate the probability of exactly 5 people checking in at Counter A in the next 15 minutes. (5 marks) b. Let X be the number of cars a mechanic repairs on a given day. The distribution of X follows. No. cars X 2 3 4 5 6 Probability 0.10 0.15 0.35 0.23 0.17 Calculate the mean and standard deviation for this probability distribution . (3 marks) Question 3 (16 marks) Marking Criteria Marks will be awarded for: ? the correct answers and appropriate detailed working including the relevant formula; ? the correct use of Excel where appropriate; ? a sentence which answers each question asked. An office supply company conducted a survey before marketing a new paper shredder designed for home use. In the survey, 75% of the people who used the shredder were satisfied with it so the company decided to market it. Assume that 75% of all people who will use the new shredder will be satisfied. a. Find the probability that for a random sample of 20 customers who purchased the new shredder, exactly 16 of these will be satisfied with it. (4 marks) b. Find the probability that for a random sample of 20 customers who purchased the new shredder, less than 14 of these will be satisfied with it. (4 marks) c. Find the expected number of dissatisfied customers in a sample of 50 customers who purchased the new shredder. (2 marks) d. Find the probability that for a random sample of 100 customers who purchased the new shredder, exactly 75 of these will be satisfied with it. (3 marks) e. Find the probability that for a random sample of 150 customers who purchased the new shredder, more than 95 will be satisfied with it. (3 marks) Hint: Use the appropriate statistical tables to determine the probabilities in parts a. and b. and use the appropriate Excel statistical function to determine the probabilities in parts d. and e. Include the Excel formula used (in d. and e.) when giving your answer. Question 4 (11 marks) Marking Criteria Marks will be awarded for: ? the correct answers and appropriate detailed working including the relevant formula; ? appropriate well labelled diagrams; ? a sentence which answers each question asked. A Professor of statistics has noted from past experience that students who do all their assignments and tutorial questions have a 98% chance of passing the final exam, and if they don’t do any of the assignments and tutorial questions they have a 15% chance of passing the final exam. The Professor estimates that 40% of the students do not do all their assignments and tutorial questions. a. Using letters of the alphabet and appropriate probability notation, define the two simple events described in this problem and their complements (4 definitions altogether) (2 marks) b. Draw a probability tree to represent the information given in the question using the letters that you used to define the simple events in part a. Label the end of each branch with the simple events and include the probabilities along each branch of the tree. (3 marks) c. What proportion of students fail the final exam? (3 marks) d. Given that a student failed the final exam, what is the probability this student did not do all their assignments and tutorial questions? (3marks) Question 5 (7 marks) Marking Criteria Marks will be awarded for: ? the correct answers and appropriate detailed working including the relevant formula; ? a sentence which answers each question asked. a. A switch board operator receives an average of 25 calls every 15 minutes. Calls are received randomly and independently. The switch board operator used the following Excel command to determine a probability 1-POISSON(20, 25, TRUE) Describe in words or write down using probability notation what probability he worked out in the context of this problem and then use Excel to evaluate it. (3 marks) b. An investment analyst collects data on shares. He notes whether dividends were paid on the shares, and whether the shares increased in price over a given period. The data collected is presented in the following table. Price increase No price increase Total Dividends paid 38 72 110 No dividends paid 85 55 140 Total 123 127 250 i) If a share is selected at random, what is the probability that it both increased in price and paid dividends? (2 marks) ii) Given that a share has increased in price, what is the probability that it also paid dividends? (2 marks) Question 6 (15 marks) Marking Criteria Marks will be awarded for: ? the correct answers and appropriate detailed working including the relevant formula and appropriate diagrams; ? appropriate well labelled diagrams; ? a sentence which answers each question asked. a. The cost of rental for a two-bedroom apartment in a particular suburb is normally distributed with a mean of $2600 per month and a standard deviation of $450. i) What is the probability that a randomly selected two-bedroom apartment in this suburb will cost less than $2300 per month? (4 marks) ii) If monthly rents for a random sample of 9 apartments in this suburb is selected, what is the probability that the mean rent for this sample is greater than $2400? (5 marks) iii) Only 5% of apartments will cost more than $x per month. Find x. (3 marks) An appropriate, well labelled diagram must be included for each part. b. A local radio station wants to survey the population in their listening area on a particular issue. They ask people to call in and give their opinion regarding the issue. From these calls the radio station draws a conclusion stating that the population in their listening area has this belief. Explain the pitfalls in this type of sampling. (3 marks) ORDER THIS ESSAY HERE NOW AND GET A DISCOUNT !!!
Our Service Charter
Excellent Quality / 100% Plagiarism-FreeWe employ a number of measures to ensure top quality essays. The papers go through a system of quality control prior to delivery. We run plagiarism checks on each paper to ensure that they will be 100% plagiarism-free. So, only clean copies hit customers’ emails. We also never resell the papers completed by our writers. So, once it is checked using a plagiarism checker, the paper will be unique. Speaking of the academic writing standards, we will stick to the assignment brief given by the customer and assign the perfect writer. By saying “the perfect writer” we mean the one having an academic degree in the customer’s study field and positive feedback from other customers.
Free RevisionsWe keep the quality bar of all papers high. But in case you need some extra brilliance to the paper, here’s what to do. First of all, you can choose a top writer. It means that we will assign an expert with a degree in your subject. And secondly, you can rely on our editing services. Our editors will revise your papers, checking whether or not they comply with high standards of academic writing. In addition, editing entails adjusting content if it’s off the topic, adding more sources, refining the language style, and making sure the referencing style is followed.
Confidentiality / 100% No DisclosureWe make sure that clients’ personal data remains confidential and is not exploited for any purposes beyond those related to our services. We only ask you to provide us with the information that is required to produce the paper according to your writing needs. Please note that the payment info is protected as well. Feel free to refer to the support team for more information about our payment methods. The fact that you used our service is kept secret due to the advanced security standards. So, you can be sure that no one will find out that you got a paper from our writing service.
Money Back GuaranteeIf the writer doesn’t address all the questions on your assignment brief or the delivered paper appears to be off the topic, you can ask for a refund. Or, if it is applicable, you can opt in for free revision within 14-30 days, depending on your paper’s length. The revision or refund request should be sent within 14 days after delivery. The customer gets 100% money-back in case they haven't downloaded the paper. All approved refunds will be returned to the customer’s credit card or Bonus Balance in a form of store credit. Take a note that we will send an extra compensation if the customers goes with a store credit.
24/7 Customer SupportWe have a support team working 24/7 ready to give your issue concerning the order their immediate attention. If you have any questions about the ordering process, communication with the writer, payment options, feel free to join live chat. Be sure to get a fast response. They can also give you the exact price quote, taking into account the timing, desired academic level of the paper, and the number of pages.