Percentage daily returns on a financial asset is modelled through a normal random variable. You want to classify returns that differ from the mean by more than 1.9 standard deviation as 'abnormal' returns and returns that differ from the mean by less than 0.64 standard deviation as 'weak' returns. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table (a) The probability of observing an 'abnormal' return is%. (Round to two decimal places including any zeros.) (b) The probability of observing a 'weak' return is%. (Round to two decimal places including any zeros.)
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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