1) a) 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?
b) What is the median number of typographical errors per page?
2. 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?
3. 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?