Fall 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. 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 20 items are to be washed with the new compound.
    1. What is the probability of satisfactory results on exactly half of the items? (5 points)

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    2. What is the probability of at least two items being found with unsatisfactory results? (8 points)

 

 

 

 

3. 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 at least 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? Hint: this is a hypergeometric problem. (14 points)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
  1. The G.PA. of Hanover College students is a continuous random variable that is distributed normally with a mean of 2.89 and a standard deviation of .50. Any student who graduates with a G.P.A. of 3.90 or better, earns the distinction of graduating summa cum laude. How many students in a college of 1095 would you expect to earn such an honor? (10 points)

 

 

 

 

 

 

 

5. The alcohol consumption of Hanover College students is a continuous random variable that is distributed normally with a mean of 7.18 beverages per week and a standard deviation of 8.85. What is the probability of a randomly selected college student having at least 5 drinks in a typical week? (10 points)

 

 

 

 

 

6. A particular make of automobile is listed as weighing 4000 pounds. Because of weight differences due to the options ordered with the car, the actual weight varies uniformly between 3900 and 4100 pounds. What is the mathematical expression for the probability density function? What is the probability that the car will weigh less than 3950 pounds? (10 points)

 

 

 

 

 

7. Weights for men between the ages of 20 and 30 have a mean m =170 pounds with a standard deviation of s =28 pounds.

    1. If a simple random sample of 40 men in this age group is to be selected and the sample mean weightcomputed, what are the values of E () and s ? (6 points)

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    2. What is the probability of a sample mean

between 160 and 180 pounds when a random sample of 50 men are drawn from the population? (8 points)

 

 

 

 

c. What role does the Central Limit Theorem play in your solution to part b? (12 points)

 

 

 

 

 

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