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?
>


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