DEPARTMENT OF MANAGEMENT SCIENCE
MSCI212: STATISTICAL METHODS FOR BUSINESS
statistical代写 Practice using statistical methods is essential to build up confidence and competence. The examples below are provided…
Week 3 Workshop statistical代写
Practice using statistical methods is essential to build up confidence and competence. The examples below are provided for you to practice on.
Simpler examples can be found in Chapters 7-12 of Stine and Foster (to get you back up to speed) if you find the questions below too difficult to start with. However the ones below are more typical of those found in courseworks and past exam papers.
Several statistical tables are provided on Moodle (under ‘General’ Information). You are encouraged to practice using them where appropriate.
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It is recommended that you tackle all the questions below at some point. At the Workshop we will concentrate on questions 5, 7 and 8, so come along to the workshop with your answers (or attempted answers) to these questions.
Q1. A retail company has six stores in a particular town which are supposed to operate at a stock-out level of 10% for all lines
(a) What is the probability that all branches will be out of a given product at the same time?
(b) What is the probability that all branches will have a given product at the same time?
(c) What is the probability that at least four of the shops have a given product at any one time?
(d) If a customer decides to visit three of the shops in search of a product, and then give up if he has had no success, what is the probability that he will not make a purchase? statistical代写
Q2. A manufacturing process for item X involves the processing of the item by two machines, A and B in that order. The item is subject to breakage in each machine. If the probability of breakage of an item is p1 in machine A and p2 in machine B;
(a) find the probability that an item will go through the system successfully.
(b) find the probability that exactly N items will go through before there is a breakage.
Q3. A market-research firm has discovered that 30% of the people who earn between $25,000 and $50,000 per year have bought a new car within the past two years. In a sample of 12 people earning between $25,000 and $50,000 per year, what is the probability that between 4 and 10 people, inclusive, have bought a new car within the past two years?
Q4. A Gallup Poll for the Air Transport Association, the airline industry’s trade association, revealed that 57% of the travellers were on business in 1982; however, in 1992, the figure was down to 37%. The airline industry likes business travellers, since they are most likely to travel at full (high) fares. statistical代写
(Source: Adapted from “Out-Faxed,” by Howard Banks, Forbes, May 10 1993, p 40.)
(a) If 10 airline travellers in 1992 were randomly selected, what is the probability that fewer than 3 travellers are business travellers?
(b) If 10 airline travellers in 1982 were randomly selected, what is the probability that fewer than 3 travellers are business travellers?Page 2 of 3
Q5. The product manager of Microsoft Canada’s consumer division found from a Canadian survey that households with children want computer software that promotes learning. She said, “In households without children, educational value is the most important factor in only 16%, but with children, the number jumps to 45%.”
(Source: Adapted from “Software Lags in Educational Needs, Survey of Owners Shows,” by David Smith, Vancouver Sun, December 17 1993, p. E13)
(a) If 20 Canadian households without children were randomly selected, how many households would you expect to value education as the most important issue in selecting computer software? Justify your choice of statistical tool.
(b) If the answer in part (a) is rounded to the nearest integer, what is the probability of obtaining this value when randomly sampling 20 Canadian households without children? statistical代写
(c) Answer part (a) for Canadian households with children.
(d) What is the probability of getting exactly the number of households expected in part (c) when randomly sampling 20 Canadian households with children?
Q6. Consider a Poisson random variable X. Find the following probabilities if the mean of X is 4.0. (a) P(X = 5), (b) P(X 4), (c) P(X 2), (d) P(3 X 6).
Q7. The number of patients needing admission each day to a hospital intensive care unit (ICU) has a Poisson distribution with a mean of 5.3.
(a) Why might it be reasonable to expect that daily numbers of patients would have a Poisson distribution rather than any other distribution?
(b) Assuming that patients only stay in the ICU for one day, what is the probability that an 8-bedded ICU will have to turn patients away on any particular day?
(c) How many beds would the ICU require to ensure that patients, on average, were only turned away one day per year? statistical代写
(d) What are the practical implications of your analyses if a hospital wishes to achieve a high level of usage for its ICU beds?
Q8. Marketing professionals say that coupons are very important to consumers. In 2000, US businesses distributed 330 billion coupons with an average face value of 71 cents, up from 307 billion coupons with an average face value of 66 cents in 1999. Approximately 70% of adult men use coupons at least once a year, compared with 85% of adult women. Assume that the value of coupons in local newspapers can be approximated by a normal distribution with a mean of 71 cents and a standard deviation of 25 cents.
(a) What is the probability that a coupon randomly selected from a local newspaper is worth at least 50 cents?
(b) What is the probability that a randomly selected coupon is worth more than $1.50? Would you consider this occurrence to be unusual?
(c) What is the probability that in a random sample of 100 adult men at least 80 use coupons at least once a year?
(d) Repeat part (c) for women and compare the probabilities.
(Source ‘Redeeming Value’, American Demographics, vol. 23, October 2001, p. 25.)Page 3 of 3
Q9. The examination committee of the Institute of Chartered Accountants passes only 20% of those who take the examination. If the scores follow a normal distribution with an average of 72 and a standard deviation of 18, what is the passing score? statistical代写
Q10. The time that a certain drug has an effect on a normal human being is considered to be exponentially distributed when a standard dose is taken. If the average length of time that the drug has an effect is 30 hours, what is the probability that any given normal person will be affected by the drug for at least 32 hours? What is the standard deviation for the length of time that the drug affects a person?
Q11. A manufacturer of heating elements for water heaters ships boxes that contain l00 elements. A quality control inspector randomly selects a box in each shipment. And accepts the shipment if there are five or fewer defective heating elements in the box. Assuming that the manufacturer has had a rate of 6% defective items, what is the probability that a shipment of heating elements will pass the inspection?
Q12. Skiers can visit Vail, Colorado, for a fraction of peak-season prices by scheduling their trips in November and December. For example, four people can share a two-bedroom condo for $50 to $80 during November and December, whereas from January to March the prices vary from $100 to $150. Assume that the distribution of these rates is uniformly distributed over these time periods. statistical代写
(a) What is the mean and standard deviation of the price of a condo for four people during November and December?
(b) During November and December, 30% of the condos for four people would be priced higher than what value?
(c) What is the mean and standard deviation of the price of a condo for four people during the January to March time frame?
(d) During January and March, 30% of the condos for four people would be priced higher than what value?
(Source: ‘Deal of the Week: Early Skiing in Vail’ Los Angeles Times, October 14, 2001, p. L3.)
