A certain mutual fund invests in both U.S. and foreign markets. Let x be a random variable that represents the monthly percentage return for the fund. Assume x has mean u = 1.9% and standard deviation o = 0.5%. (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-- distribution is approximately normal. the --Select-- (b) After 6 months, what is the probability that the 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.)

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
icon
Concept explainers
Question

Hi how would u figure this out?

A certain mutual fund invests in both U.S. and foreign markets. Let x be a random variable that represents the monthly percentage
return for the fund. Assume x has mean u = 1.9% and standard deviation o = 0.5%.
(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--
the --Select---
distribution is approximately normal.
(b) After 6 months, what is the probability that the 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.)
Transcribed Image Text:A certain mutual fund invests in both U.S. and foreign markets. Let x be a random variable that represents the monthly percentage return for the fund. Assume x has mean u = 1.9% and standard deviation o = 0.5%. (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-- the --Select--- distribution is approximately normal. (b) After 6 months, what is the probability that the 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.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Knowledge Booster
Fundamentals of Algebraic Equations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman