An investment portfolio contains stocks of a large number of corporations. Over the last year the rates of retum on these corporate stocks followed a normal distribution with mean 14.6% and standard deviation 7.5% a. For what proportion of these corporations was the rate of return higher than 18%? b. For what proportion of these corporations was the rate of return negative? c. For what proportion of these corporations was the rate of return between 10% and 20%? E Click the icon to view the standard normal table of the cumulative distribution function. a. The proportion of corporations whose rate of return was higher than 18% is. (Round to four decimal places as needed.) b. The proportion of corporations whose rate of return was negative is (Round to four decimal places as needed.) c. The proportion of corporations whose rate of return was between 10% and 20% is. (Round to four decimal places as needed.)

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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!