1. Define the following terms: random experiment, sample space, random variable, expected value.
   
2. You are manufacturing glass plates, 2 m X 1 m in size. Flaws in the plates occur at random at a rate of 0.05 m^-2. Plates with one or more flaws will be scrapped and melted down.
   (a) What percentage of all plates will be scrapped? State any assumptions you make.
   (b) If you produced 20 plates in one hour, what is the probability that at least 3 of them will have to be scrapped? State any assumptions you make.
   (c) If a plate is to be scrapped, what is the probability that it has only one flaw?
   
3. Apples from a given orchard have a mean weight of 263 g and a standard deviation of 21 g. They are packed 20 to a bag. What is the probability that the total weight of a bag will be less than 5 kg? State any assumptions you make. [Note that F(2.768) = 0.9972.]
   
4. If a random variable X can take values 1, 2.5, 3, 500 with probabilities 0.1, 0.35, 0.5, 0.05, respectively, find the median, mean, variance and standard deviation of X.

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Statistics 3N03