Help!! CONCLUDE: Select the correct conclusion based on the results.There is about a 13% chance of getting average returns over 10% and a 3% chance of getting average returns lessthan 5%.There is about a 64% chance of getting average returns over 10% and a 1% chance of getting average returns lessthan 5%.O There is about a 33% chance of getting average returns over 10% and a 1% chance of getting average returns lessthan 5%.There is about a 75% chance of getting average returns over 10% and a 9% chance of getting average returns lessthan 5%. STATE: Andrew plans to retire in 40 years. He plans to invest part of his retirement funds in stocks, so he seeks outinformation on past returns. He learns that from 1966 to 2015, the annual returns on S&P 500 had mean 11.0% andstandard deviation 17.0%.PLAN: The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even amoderate number of years is close to Normal. We can use the Central Limit Theorem to make an inference.SOLVE: What is the probability, p1, assuming that the past pattern of variation continues, that the mean annual return oncommon stocks over the next 40 years will exceed 10% ? (Enter your answer rounded to two decimal places.)Pi =What is the probability, p2, that the mean return will be less than 5% ? (Enter your answer rounded to two decimalplaces.)P2 =

Name: Help!! CONCLUDE: Select the correct conclusion based on the results.Th
Uploaded: 2024-03-05T11:52:21.000Z
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Description: Help!! CONCLUDE: Select the correct conclusion based on the results.There is about a 13% chance of getting average returns over 10% and a 3% chance of getting average returns lessthan 5%.There is about a 64% chance of getting average returns over 10%

Answered: STATE: Andrew plans to retire in 40…

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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Help!!

CONCLUDE: Select the correct conclusion based on the results.
There is about a 13% chance of getting average returns over 10% and a 3% chance of getting average returns less
than 5%.
There is about a 64% chance of getting average returns over 10% and a 1% chance of getting average returns less
than 5%.
O There is about a 33% chance of getting average returns over 10% and a 1% chance of getting average returns less
than 5%.
There is about a 75% chance of getting average returns over 10% and a 9% chance of getting average returns less
than 5%.

STATE: Andrew plans to retire in 40 years. He plans to invest part of his retirement funds in stocks, so he seeks out
information on past returns. He learns that from 1966 to 2015, the annual returns on S&P 500 had mean 11.0% and
standard deviation 17.0%.
PLAN: The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a
moderate number of years is close to Normal. We can use the Central Limit Theorem to make an inference.
SOLVE: What is the probability, p1, assuming that the past pattern of variation continues, that the mean annual return on
common stocks over the next 40 years will exceed 10% ? (Enter your answer rounded to two decimal places.)
Pi =
What is the probability, p2, that the mean return will be less than 5% ? (Enter your answer rounded to two decimal
places.)
P2 =

Expert Solution

Step 1

Let the returns be given by X.

Given,

$X ~ N (11, 17^{2})$

Let $X$ be the mean returns over a period of 40 years.

So,

$X ~ N (11, \frac{17^{2}}{40})$

to calculate $p_{1} = P [X > 10]$

$P [X > 10] = P [\frac{X - 11}{\sqrt{\frac{17^{2}}{40}}} > \frac{10 - 11}{\sqrt{\frac{17^{2}}{40}}}] = P [Z > - 0.372] = 1 - P [Z < - 0.372] = 1 - ϕ (- 0.372) S i n c e t h e d i s t r i b u t i o n i s g i v e n t o b e s y m m e t r i c, ϕ (- z) = ϕ (z) = 1 - ϕ (0.372) = 1 - 0.64431 = 0.35569 v a l u e o b t a i n e d f r o m s \tan d a r d n o r m a l d i s t r i b u t i o n t a b l e s .$

Hence,

$p_{1} = 0.36$ (rounded off to two decimal places)

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