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               Econ 120A, Winter 1998  --  Homework #3 (5%)
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This homework is due at 11:10 am on the last day of class.  Papers
turned in at the end of the class will carry a 25% penalty and THOSE
TURNED IN LATER WILL NOT BE ACCEPTED.  As before, team up with others
(maximum 3 persons per team) and submit a single paper with all names.


I.   A rental car company operates between two cities A and B.  In city
     A it has "a" Fords and "b" Chevrolets.  In city B it has "c" Fords
     and "d" Chevrolets.  A customer picks a car at random from city A,
     drives it to city B, and leaves it there.  A second customer then
     chooses a car at random from city B.  What is the probability that
     it is a Ford?

II.  You need 18 computer memory chips to install in the motherboard of
     a microcomputer.  You order 20 memory chips because you know that
     10 percent of all chips are defective.  What is the probability that
     your computer will work, that is, have enough working chips?  Show
     all your work.  Refer to Table A.6 in the above text book.

III. An instructor in Statistics decides to "grade on the basis of a
     normal curve", that is, assume that grades are normally distributed.
     She gives 5 percent A's, 20 percent B's, 50 percent C's, 20 percent
     D's, and 5 percent F's.  If the population mean score is 75 and
     the standard deviation is 10, what are the numerical grades that
     divide the five letter grades?   You can either use the standard
     normal table I gave in class or use Table A.1 in my book.
 
IV.  The bakery section of a grocery store prepares a number of
     decorated cakes at the beginning of each day.  For each cake sold
     the store makes a profit of 3 dollars and for each cake not sold it
     loses 9 dollars because of labor and material costs not covered.
     Suppose the number of cakes demanded in a day has the discrete
     uniform distribution f(x) = 1/10  for x = 1, 2, ..., 10.  If the
     bakery stocks n cakes (n <= 10), calculate the expected profit.  To
     maximize expected profit what is the optimum n?

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