STATISTICS 3N03/3J04

 

Test #2 * 2005-11-04

 

Instructions

 

Aids permitted: any calculators, any mathematical or statistical tables, one sheet of notes (8.5" x 11", one side only).

 

Questions

 

  1. Suppose that the average weight of people is 66 kg and the standard deviation is 10 kg. If an elevator can take a maximum load of 750 kg, and people get on independently of each other, and we want the probability of overload to be less than 0.1%, how many people can be allowed on at one time? State any assumptions you make. Why would your calculation be invalid if you knew that there were "weight-watchers" meetings in the building every day?

 

  1. Production Line A produces twice as much cable as Production Line B. Flaws in the cable occur randomly, independently of each other, at an average rate of 1 flaw per 100 m in Line A and 2 flaws per 100 m in Line B. If a randomly-chosen 500 m roll of cable has 6 flaws, what is the probability that it came from Line A?

 

  1. The ball bearings you produce have a mean diameter of 5 mm and a standard deviation of 0.1 mm. A ball bearing will be acceptable if it is between 4.7 and 5.3 mm in diameter. In a lot of 10000 ball bearings, what is the probability that more than 35 will be unacceptable? What would you have to do to achieve six-sigma quality in this process?

 

  1. Define the following terms: statistic, sampling distribution. What sampling distribution did W.S. Gosset discover? Who was his employer at the time? What do the initials W.S. stand for?
Statistics 3N03/3J04