Q.6: A pharmaceuticals plant sets out pills of a particular medicine with a batch size 20000. Suppose that the probability of any one pill coming out bad is 0.0004: (1) What is the probability that there are between 4 and 8 bad pills in any given batch? (1I) If someone wanted to write a definition for a suitable random variable, what would you be? (III) If someone had asked you to approximate your answer to the one in (1), how would you go about doing it? (IV) Justify, through a convincing argument, that your answer to part (III) is sound and correct.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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