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Question 2: A company generally purchases large lots of a certain type of laptop computers. A...

Question 2: A company generally purchases large lots of a certain type of laptop computers. A method is used that rejects a lot if more than 2 defective laptops are found in a lot. Past experience shows that 10% laptops are defective.   

  1. What is the probability of rejecting a lot of 20 units?
  2. What is the probability that in a batch of 20 laptops between 3 and 5 (inclusive) laptops are defective?
  3. On the average how many defective laptops are there in a lot of 20 laptops?

Question 3: The number of cars arrive at a gas station follows a Poisson distribution with a rate of 10 cars per hour.

  1. Calculate the probability that 2 to 4 (inclusive) cars will arrive at this gas station between 10:00 am and 10:30 am.
  2. What are the mean and standard deviation of the distribution you have used to answer part a?

Question 4: The time to finish the Abu Dhabi Grand Prix Formula one (F1) motor race is normally distributed with a mean of 106.47 minutes and a standard deviation of 0.376 minutes.

  1. What is the probability that the finishing time of a F1 car in the race selected at random at most 106.375 min?
  2. Find the probability that the finishing time of a randomly selected F1 car in the race is between 106.375 min and 107.065 min.
  3. What is the finishing time (t0) such that 95% of the F1 racing cars in the population have finishing time at most t0?
  4. The probability that each of the F1 cars will not finish the race for any reason is 0.12. Given that there were 25 qualified F1 cars in a race, find the probability that at most 5 of these cars will not finish the race.
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