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[Step-by-Step] [8 Marks] A psychologist tests seventh grade students on basic word association skills and number pattern recognition skills. Let W be the

Question: [8 Marks]

  1. A psychologist tests seventh grade students on basic word association skills and number pattern recognition skills. Let W be the event a student does well on the word association test. Let N be the event a student does well on the number pattern recognition test. For a randomly selected student, assume that the following probabilities are given:

  1. What is the probability the randomly selected student does well on the word association test?
  2. What is the probability the randomly selected student does well on at least one of the tests?
  3. If the randomly selected student does well on the number pattern recognition test, what is the probability he or she will also do well on the word association test?
  4. Are the events W and N mutually exclusive? Justify your answer.
  5. Are the events W and N independent?

(b) A Statistics Department is contacting alumni by telephone asking for donations to help fund a new computer laboratory. Past history shows that 80% of the alumni contacted in this manner will make a contribution of at least $50. A random sample of 20 alumni is selected. Let x represent number of alumni that makes at contribution of at least $50.

  1. What is the probability that exactly 15 alumni will make a contribution of at least $50?
  2. What is the probability that between 14 and 18 alumni, inclusively, will make a contribution of at least $50?
  3. What is the probability that less than 17 alumni will make a contribution of at least $50?
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