A certain mutual fund invests in both U.S. and foreign markets. Let xa random variable that represents the monthly percentage return for the fund. Assume x has mean u = 1.9% andstandard deviation o = 0.3%.(a) The fund has over 175 stocks that combine together to give the overall monthly percentage return x. We can consider the monthly return of the stocks in the fund to be asample from the population of monthly returns of all world stocks. Then we see that the overall monthly return x for the fund is itself an average return computed using all 175stocks in the fund. Why would this indicate that x has an approximately normal distribution? Explain. Hint: See the discussion after Theorem 6.2.The random variable-Select-v is a mean of a sample size n = 175. By the -Select-v, the -Select- distribution is approximately normal.(b) After 6 months, what is the probability that thẹ average monthly percentage return x will be between 1% and 2%? Hint: See Theorem 6.1, and assume that x has a normaldistribution as based on part (a). (Round your answer to four decimal places.)(c) After 2 years, what is the probability that 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?O YesO NoWhy would this happen?as the-Select-- v increases.The standard deviation -Select--(e) If after 2 years the average monthly percentage return was less than 1%, would that tend to shake your confidence in the statement that u = 1.9%? Might you suspect that uhas slipped below 1.9%? Explain.O This is very likely if u = 1.9%. One would suspect that u has slipped below 1.9%.O This is very unlikely if u = 1.9%. One would suspect that Lu has slipped below 1.9%.O This is very unlikely if u = 1.9%. One would not suspect that u has slipped below 1.9%.19% One would not suspect that u has slinned below 1.9%US 2 • A 2:52O This is very likely if uhp

* Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at…

p) After 6 months, what is the p stribution as based on part (a). =) After 2 years, what is the pro d) Compare your answers to pa O Yes O No Why would this happen? The standard deviation (e) If after 2 years the average has slipped below 1.9%? Explair O This is very likely if u = if Lu

p) After 6 months, what is the p stribution as based on part (a). =) After 2 years, what is the pro d) Compare your answers to pa O Yes O No Why would this happen? The standard deviation (e) If after 2 years the average has slipped below 1.9%? Explair O This is very likely if u = if Lu

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

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!

Question

A certain mutual fund invests in both U.S. and foreign markets. Let x
a random variable that represents the monthly percentage return for the fund. Assume x has mean u = 1.9% and
standard deviation o = 0.3%.
(a) The fund has over 175 stocks that combine together to give the overall monthly percentage return x. We can consider the monthly return of the stocks in the fund to be a
sample from the population of monthly returns of all world stocks. Then we see that the overall monthly return x for the fund is itself an average return computed using all 175
stocks in the fund. Why would this indicate that x has an approximately normal distribution? Explain. Hint: See the discussion after Theorem 6.2.
The random variable
-Select-v is a mean of a sample size n = 175. By the -Select-
v, the -Select- distribution is approximately normal.
(b) After 6 months, what is the probability that thẹ average monthly percentage return x will be between 1% and 2%? Hint: See Theorem 6.1, and assume that x has a normal
distribution as based on part (a). (Round your answer to four decimal places.)
(c) After 2 years, what is the probability that 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?
O Yes
O No
Why would this happen?
as the
-Select-- v increases.
The standard deviation -Select--
(e) If after 2 years the average monthly percentage return was less than 1%, would that tend to shake your confidence in the statement that u = 1.9%? Might you suspect that u
has slipped below 1.9%? Explain.
O This is very likely if u = 1.9%. One would suspect that u has slipped below 1.9%.
O This is very unlikely if u = 1.9%. One would suspect that Lu has slipped below 1.9%.
O This is very unlikely if u = 1.9%. One would not suspect that u has slipped below 1.9%.
19% One would not suspect that u has slinned below 1.9%
US 2 • A 2:52
O This is very likely if u
hp

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