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An insurance company has 32,000 clients, and 5% of their clients submitted a claim in the past year.

  1. An insurance company has 32,000 clients, and 5% of their clients submitted a claim in the past year. A sample of 2,000 clients will be taken and how many of them have submitted a claim in the past year will be determined. What is the sampling distribution of pˆ, the sample proportion of claimants?
  2. A student is taking a multiple-choice exam consisting of 10 questions in which each question has 4 choices. Assuming that she has no knowledge of the correct answer to any of these questions she has decided on a strategy in which she will place 4 balls into a box. She randomly selects 1 ball for each question and replaces the ball back into the box. The marking on the ball selected will determine her answer to each question. i) What is the probability that she will get 4 or more questions right in order to pass the exam? ii) Find the expected number and the standard deviation of the number of questions she will get correct?

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