MATH 230

TEST III

Fall 1999

Bellamy & Williford


Problems 1-5 count 20 points each. You must show all your work to receive more than half credit on any problem.

  1. 20 points
    1. Suppose X is the number of successes in 100 Bernoulli trials with probability tex2html_wrap60 of success. Find the expected value, variance, and standard deviation of X .
    2. Let Y be the number of heads in 100 tosses of a fair coin with X as in part (a). Determine which is larger E(X) or E(Y). Then determine which of Var(X) OR Var(Y) is larger.

  2. 20 points
    A sales rep will call on either Bill or Elaine this afternoon. If she calls on Bill, the probability of making a sale is tex2html_wrap67. If she calls on Sue the potential amount of the sale is larger, but the probability of making a sale is only tex2html_wrap68. The rep is equally likely to call on either one but does not have time to call on both. You are this rep's supervisor and you get an incomplete voicemail saying that she made a sale, but not to whom or for how much. What is the (conditional) probability she called on Bill instead of Elaine?

  3. 20 points
    Solve using matrix row reduction:

      tex2html_wrap69

      Then compute tex2html_wrap70.

  4. 20 points
    Perform whatever row operations (indicating each one) are necessary to get the following matrix into reduced form:


    displaymath105

  5. 20 points
    Set up as a system of linear equations (but do solve) the following problem. Be sure to define precisely what your unknowns are. (Recall that a ton is 2000 pounds.)

    The Natural Fertilizer Company makes three types of fertilizer: 20 - 5 - 5 for lawns, 10 - 15 - 10 for gardens, and 5 - 5 - 5 for trees. The numbers in each case refer to the percentage by weight nitrates, phosphates, and potash, respectively. The fertilizer is packed in 100-pound sacks. The company has the following amounts of raw materials on hand: 7 tons of nitrates, 4 tons of phosphates, and 3 tons of potash.

    They need to use up all the raw materials in stock prior to moving their factory to a new location. How much of each type of fertilizer should they make. (There is more than one correct way to set this up; any correct way is OK.)

  6. BONUS: 15 quiz points
    An urn contains 5 red and 5 green balls. Four balls are drawn randomly, one after another, without replacement.

    1. Find the probability all balls drawn are the same color.
    2. Find the conditional probability the first two were both red given that the last two were both green.



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