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MTH362 Fall 2000 Sample problems for test 1

Note: This is a list of sample problems. The exam will less problems.

  1. Consider the following data:
    22    35    43    36    38     38    27    29     38     22

    Produce a relative frequency histogram. Use class intervals [20,24],[25,29],[30,34],[35,39],[40,44].
  2. Calculate the mean, median, variance and standard deviation of the data given in the previous question.
  3. Define the following terms: Experiment, outcome, sample space, event, trial, random variable.
  4. Two special dice with 4 faces each, labeled 1,2,3,4 are rolled, and the numbers that turn up are recorded.
    a)Write down the sample space of this experiment.
    b)What is the probability of the event E="Both dice turn up the same number"?
  5. Suppose $A$ and $B$ are events such that $P(A)=0.25$, $P(B)=0.5$ and $P(A\cap B) = 0.05$. What is the numerical value of (a) $P(A\cup B)$, (b) $P(A^c )$, (c) $P(A^c \cup B^c)$.
  6. A box has 4 right handed screws and 6 left handed screws. One screw is taken out at random and put aside, and then another screw is taken out. What is the probability of getting
    a) Two right handed screws? b)A left handed and a right handed screw?
  7. A box has 4 right handed screws and 6 left handed screws. One screw is taken out at random and put back in the box, and then a screw is taken out again. What is the probability of getting
    a) Two right handed screws? b)A left handed and a right handed screw?
  8. Each time a team plays, it has a probability of winning equal to 0.45. What is the probability of the following events: a) Three wins in a row. b) At least two wins in 10 matches.
  9. a)How many license plates are there with 4 letters? (repetition allowed) b)How many if no repetition is allowed? c)How many if four letters (no repetition) are followed by 3 digits (no repetition)?
  10. How many committees of 4 people can be formed from a group of 30 people? How many selections of secretary, president and controller are possible when they are taken from a group of 30 people?
  11. A die is rolled 20 times. What is the probability of getting exactly two 6's?
  12. 2 percent of the items produced by a machine are defective. What is the probability that when 50 items are produced, at most one item is defective? Solve first by using the binomial distribution model. Then solve the problem again to approximate the answer using the Poisson distribution model.
  13. A random variable X is normally distributed with mean 4.0 and standard deviation $\sigma = 0.75$. Use the table to find the following probabilities:
    a) $P(X \leq 3)$,
    b) $P(3 \leq X \leq 5)$,
    c) $P(5 \leq X)$
  14. The length $X$ of pipes produced by a machine is normally distributed with mean 60 in. and standard deviation 1.5 in. If a pipe is acceptable if its length is within 2 in. from the mean, what percent of the pipes produced by the machine is acceptable?



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Orlando Merino
2000-09-29