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ECON 227 Assignment 2 Misc. Problems




Question;2. A group;of 60 stocks includes 36 that have increased in value since November 1st;and 24 that have decreased since November 1st.;a) A.J.Jones;has taken a random sample of 6 stocks from the group, and would like to;calculate (before looking to see, of course) the probability of having picked;at least 4 of the stocks that have increased in value. He can?t remember whether to use the binomial;or hypergeometric formula. Help him out;by demonstrating that for three decimal places of accuracy he can use either;one.;b) If the;stocks are examined in a random manner one-by-one, what is the probability that;the first three will all be stocks that have increased?;c) If the;stocks are examined in a random manner one-by-one, Let X be the number of;stocks that have been examined when the first decreased-value stock is;found. Find the median value of X.;4. a) Banks only accept coins for deposit if;they are rolled in;specified;amounts. Pennies, for example, are to be in rolls of 50. A Canadian bank has;checked the 200 rolls of pennies they have on hand. Only 12 of the rolls contained all Canadian;pennies: the rest all had at least one American penny. Altogether in the 200 rolls, about how many;American pennies are there?;b);What is the median;number of American pennies in a roll?;c);N.B. This c) part has;nothing to do with the a) part.;The;number of cars passing a checkpoint is treated by a consulting firm as having a;Poisson distribution with a mean of 20 per minute. What does the firm consider the standard;deviation in interarrival times to be?;5. a) In;an office employees have been categorized according to;seniority and age. Some of the results are cross-tabulated;below.;Management;White-collar;Aged;50 or more;8;32;Aged;less than 50;12;28;i) If;10 workers from the office are selected at random;what is the probability of at least 3;white-collar workers amongst those chosen?;ii) If 10 workers aged less than 50 are;selected at random from the office, what is the probability of at most 3;management workers amongst those chosen?;b) A thick book with 1200 pages has quite a;few typographical;errors.;There are only 180 pages without typographical errors in the whole;book. If typographical errors occur;randomly, about how many pages in the book have three typographical errors?;d);What is the;median number of typographical errors per page?;6. The length of time taken to learn a set;of instructions may be treated as having an exponential distribution with a;mean of 24 minutes. There is only one;copy of the instructions, so as soon as one person has completed the learning;process, the next person begins, with no intervening gap.;a) What proportion of those learning take;between 20 and 30 minutes?;b);What is the 60th percentile of learning times?;c) What is the probability that at least;three persons complete the learning process in a single one-hour period?;8. A.J.Jones;works at Acme Economics Think Tank. The;employees? cafeteria offers a daily special called Box Lunch Surprise for;$6.50. The cook has a limited;repertoire, so that the surprise lunch is always either a ploughman?s lunch;(cheese and bread) or a grilled-cheese sandwich with fries. On December 19th, 2011 there are;20 unmarked box lunches, of which there are 8 ploughman?s lunches and 12;grilled-cheese sandwiches. The boxes are;arranged in a random fashion so that there is no way of knowing what is in a;box before it is bought. Once opened, a;box lunch cannot be returned.;a) Today;A.J.Jones has decided to buy a Box Lunch Surprise for each of the 4 members of;his team. What is the probability that;there will be two ploughman?s lunches and two grilled-cheese sandwiches?;b) Two;members of the team will absolutely not eat grilled cheese. How many lunches will A.J. have to buy in;order to have at least a 90% probability of including two ploughman?s lunches;(or more)?;c) A.J. buys;boxes one at a time until he gets three grilled cheese. What is the probability that he will have to;spend $45.50 in order to achieve his goal?;9. A;time-and-motion-study consultant has been hired at Eurelia Industries;Limited. She has identified a certain;work station as a bottleneck in production.;Initial data suggest that the times required for processing pieces at this;station may be treated as having an exponential distribution with a mean of;three hundred seconds.;a) If fifty;pieces are processed, about how many of them take between two hundred forty and;three hundred sixty seconds to process?;b) What is;the probability that more than the mean number of pieces will be processed in a;ten-minute period?;c);What is the median;processing time at the station?;d) What;proportion of processing times are within two standard deviations of the mean?


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