Winter 1998 EXAM 2

You may not use any extra sheets of paper to answer the following questions. Whenever possible, show your work for potential partial credit. NOTE: When performing numerical calculations, keep at least 4 digits after a decimal. (i.e., do NOT round .2265 to .23 or .227)

  1. Using probabilities, explain the difference between two events that are mutually exclusive and two events that are independent. (6 points)

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  2. Events A and B are mutually exclusive. Can they be independent as well as mutually exclusive? Explain. (6 points)

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  3. Measuring the time in which it takes a luge (and rider) to complete the luge run in the Winter Olympics can be thought of as an experiment. What is the random variable (x) associated with this experiment? Is x a continuous or discrete random variable? Why? What values can the random variable assume? (8 points)

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  4. There are 69 male (M) students in a sample of 118 Hanover College students. There are a total of 66 students who are majoring in the social sciences (SS) and 26 majoring in both the natural sciences (NS) and in the humanities (H). Of the 66 majoring in the social sciences, 42 are male. There are 15 male natural science majors and 12 male humanities majors.
    1. What is the probability of being female (F)? (2 points)

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    2. Find P(MÇSS) and find P(SSï M). (4 points)

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    3. Find P(Fï SS). Hint: this is a Bayesian probability. (5 points)

 

  1. Describe the situation in which a Poisson probability function would be useful. What are the two assumptions necessary for the Poisson distribution to be applicable? (12 points)

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  2. A new clothes-washing compound is found to remove excess dirt and stains satisfactorily on 88% of the items washed. Assume that 10 items are to be washed with the new compound.
    1. What is the probability of satisfactory results on all 10 items? (3 points)

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    2. What is the probability of at least two items being found with unsatisfactory results? (4 points)

 

 

 

 

  1. Williams Company has observed that calculators fail and need to be replaced at the rate of 3 every 25 days.
    1. What is the expected number of calculators that will fail in 30 days? (4 points)

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    2. What is the probability that at least 2 will fail in 50 days? (6 points)

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    3. What is the probability that exactly 3 will fail in 10 days? (5 points)

 

 

  1. Suppose 8 out of the 12 members in the most recent edition of the Summer Olympic "Dream Team" endorse Nike basketball shoes. Reebok, the company that designed and contributed "Team USA" warm-ups for the entire team, sponsors the rest of the players. At the conclusion of each game, 3 players are chosen to speak to the media. With Reebok’s financial interest, they would like a majority of the 3 to be wearing their Reebok warm-ups. How would you advise the marketing department on the likelihood of this event? (8 points)

 

 

 

 

 

 

 

9. The G.PA. of Hanover College students is a continuous random variable that is distributed normally with a mean of 2.7924 and a standard deviation of .4796. Any student who graduates with a G.P.A. of 3.90 or better, earns the distinction of graduating summa cum laude. What is the probability that a student will earn such an honor? (7 points)

 

 

 

 

10. Explain the difference between the normal probability distribution and the standard normal probability distribution. What is the critical role of the standard normal probability distribution in calculating probability exercises like the one above? (10 points)

 

 

 

 

 
  1. The age of Hanover College students is also distributed normally, with a mean of 20.243 and a standard deviation of 1.0407. If the youngest professor on campus were 27 years old, what is the probability that this professor would have a student older than he? (10 points)

 

 

 

 

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