Suppose the money return on stocks from the European Stock Exchange follows a normal distribution with 7% rate of return (the mean) with a dispersion of 3% (standard deviation). (A) How many stocks will earn a return between 4% and 8% if there are 1000 firms listed on the stock exchange? (B) To the nearest percent, find the probability of a stock earning 0% or less per year (i.e. not making money or losing money)? If there are 1,000 firms listed on the stock exchange, then how many firms will not make any money or lose money? (C) To the nearest percent, find the probability of a stock earning 14% 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 14% or higher? (D) What rate of return would put a firm in the top 15%?
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!
Suppose the money return on stocks from the European Stock Exchange follows a normal distribution with 7% rate of return (the mean) with a dispersion of 3% (standard deviation).
(A) How many stocks will earn a return between 4% and 8% if there are 1000 firms listed on the stock exchange?
(B) To the nearest percent, find the probability of a stock earning 0% or less per year (i.e. not making money or losing money)? If there are 1,000 firms listed on the stock exchange, then how many firms will not make any money or lose money?
(C) To the nearest percent, find the probability of a stock earning 14% 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 14% or higher?
(D) What rate of return would put a firm in the top 15%?
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