The Rate of Return for firms on the stock market is normally distributed with a 7.5% average rate of return (the mean) with a standard deviation of 2.5%. (A) What proportion of firms will earn a return between 4% and 8%? (B) To the nearest percent, find the probability of a firm earning 3% or less per year? If there are 1,000 firms listed on the stock market, then how many firms earn a return of less than 3% a year? (C) To the nearest percent, find the probability of a firm earning 8% return in a year. If there are still 1,000 firms listed on the stock market, then how many firms will earn a return of 8% or higher?
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!
The Rate of Return for firms on the stock market is
(A) What proportion of firms will earn a return between 4% and 8%?
(B) To the nearest percent, find the probability of a firm earning 3% or less per year? If there are 1,000 firms listed on the stock market, then how many firms earn a return of less than 3% a year?
(C) To the nearest percent, find the probability of a firm earning 8% return in a year. If there are still 1,000 firms listed on the stock market, then how many firms will earn a return of 8% or higher?
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