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QUERY Please find below four statistics/probability problems from an undergraduate statistics course. Stats is not my strength, and I would greatly appreciate any help you may be able to provide. Please e-mail tips, solutions etc. to [log in to unmask] Thank You. >1) A producer of screws knows from experience that his/her packaging >machines do not work flawlessly. In 2% of all cases the packaging machine >puts less screws in a box than indicated on the package. A major retailer >buys 400 boxes conditionally on not finding more than 10 boxes which >contain not enough screws. What is the probability that there are 10 boxes >containing not enough screws? What is the probability that there are more >than 10 boxes containing not enough screws? What is the probability that >the larger retailer returns the shipment? > > >2) (a)The pesonnel office of a large company in New England found that 10% >of its 5000 employees changed their address in 1984. This office wants to >know if the percentage has changed in 1988 and therefore conducts a survey. > Assume throughout this question that 10% have changed their address in >1988. What is the probability that in a sample size 10 you will find 1 >person who has changed his/her address? What is the expected value if you >repeatedly sample with sample size 10? > > (b)Finally, let us assume that the personnel office asked 100 different >employees. What is the probability that you find less than 5 employees who >have moved? Assuming that the population probability has changed to 3% >movers, what is the probability that less than 5 employees indicate that >they have a new address (sample size 100)? > > >3) A random sample of college students were asked to rate their courses on >a scale of 1 to 10 (10 being best) and to state their grade in the course >on a scale of 1 to 12 (A=12, A-=11, and so on). The average rating was >5.53 and the average grade 9.69. A least squares regression of rating (Y) >on grade (X) yielded: > > Y=2.14+0.79 > (2.91)(0.296) > () = standard deviations. > >What does a least squares regression tell us that comparison of the average >values, 5.35 versus 9.69, does not? How would you interpret the estimate >0.79? Is the estimated relation statistically significant? Do you think >that grades determines rating or that rating determines grade? What >difference does it make to a regression equation? > > >4) A firm finds that 1,500 of its employees arrives at work by car, and >that 20% of the cars have serious safety flaws. It is decided to pass out >pamphlets on safety hazards in cooperation with the local police >department. To test the success of this action, management takes a sample >of 100 vehicles and finds that 12 still do not satisfy standard safety >requirements. What is the probability to find 12 or less defective cars if >the population has not changed? Do your calculations using (i) n*pi as the >expected value, (ii) pi as the expected value. What is the probability >finding less that 2 flawed vehicles in a sample of 10, assuming that there >are no changes in the population? > %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%