pose x has mean ? = 1.5% and standard deviation ? = 1.3%. (a) Let's consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all European stocks. Is it reasonable to assume that x (the average monthly return on the 300 stocks in the fund) has a distribution that is approximately normal? Explain. , x is a mean of a sample of n = 300 stocks. By the , the x distribution approximately normal. (b) After 9 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)
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!
A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 300 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has
, x is a mean of a sample of n = 300 stocks. By the , the x distribution
(b) After 9 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)
(c) After 18 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)
(d) Compare your answers to parts (b) and (c). Did the probability increase as n (number of months) increased? Why would this happen?
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